CheopsATLAS ¦ Universums Historia

CHEOPS ATLAS ¦ UNIVERSUMS HISTORIA | a production 2020I1 | Senast uppdaterade version: 2024-03-01 · Universums Historia

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NatCH ¦ PetrieQuotes ¦ HowSTART ¦ ENTER ¦ MainConstruct ¦ PetrieDAngles ¦ CheopsATLAS-Pyramids ¦ CheopsATLAS-TNED ¦ CheopsAT ¦ Resolution 217 ¦ C14darting

Cheops Atlas Begin

THOUSANDS OF YEARS BACK FROM HERE some established sources claim, in some parts, a no-easy-

explainable glaciation history — only over the northern Earth part. THAT promotes a further GeoATLANTIS

investigation. See a special treatise glaciation article in this CheopsATLAS series modern rebellious parvenu.

— Calling ATLANTIS .. ello .. ello .. 222 .. 333 .. ¦ ATLANTIS ¦ GTursprunget2019 ¦ AtlantisAPPENDIX ¦

— Roger .. Roger .. Mayday .. Mayday .. A GEOATLANTIS might EXPLAIN some GLACIATION VARIATIONS — GeoATLANTIS NORTHERN HEMISPHERE GLACIATION VARIATIONS

— What’sUp?

BackGround: Name and Term

• Background.

— The naming or THE TERM CHEOPS RECTANGLE is my own early label: Tracking the original math connection bd=h² back to The Cheops Pyramid was clarified during a shorter library literature research (See sw. HistoryBackground [around the time when Intel presented its first microprocessor 8080]).

The term CHEOPS RECTANGLE was adopted by this author after a late 20th century detective search — in libraries: The most early known mentioning of the unique and very geometrical-developing useful connection bd=h². It was rhetorically used by Galileo Galilei, Apollonios and Pythagoras, further backwards mentioned as an Egyptian ancient form connected to the Cheops Pyramid.

— We respect that tradition here, and adopt the term to it.

IntroEX:

————————————————————————————————————————————

k0 ¦ GOLDEN SECTION BODY — R ¦ 18 ¦ rJ ¦ rJCR¦b16

ENTER — MiUNIT. These and others provably breach modern archaeological ideas of the origins: exact quantitative proofs. A correspondingly exposed building plan appears: as so extracted — from the rJCIRCLE complex: GOLDEN SECTION CHEOPS RECTANGLE MATH.

We study the details: THE TWO PYRAMID CONSTRUCTIVE AGENTS.

CONTRACTED CONSTRUCT: Main OVERVIEW — The Cheops Pyramid proof of a Contracted Construct ¦

RECURRING CONSTANTS @3 SITES — The cSIDE

The GOLDEN SECTION Cheops Rectangle Complex ON the actual physical Petrie 1833 measured CheopsPyramid

Central connecting construction point

The ArcTan½ LINE

Guaranteed construct sealing

DEFINING PETRIE’s MEASURES

Enter

Petrie’s D angles

AT SOUTH Gallery end

No uninitiated

will understand

The CONTRACTED CONSTRUCT

THE 7 construct POINTS

THE 2 PYRAMID AGENTS

The Main Construct

THE 18th ROOF

The D point

The Great Step

As we know:

— There are no real or DIRECT measures of the Golden Section (CHEOPS RECTANGLE) details INSIDE the Petrie 1883 measured The Great Cheops Pyramid (conv. Khufu Pyramid, after late modern Egyptology consensus). As injured as the building is in our days, there is neither such a measure outside it.

— THROUGH the Golden Section Paragon Arithmetics and Geometry, however, all Petrie measuring points and their coordinates relative the Petrie discovered Pyramid’s ½ square base (PetrieCP¦b=4534,40’’ ± 0.25) can — has shown to — be calculated with excellent precision. That we will expose in this presentation — on the shoulders of all those who have made contributions to the Petrie established Cheops Pyramid metrics, their tolerances and presentations.

To be noted: Several later 20th centuries sources have verified and asserted Flinders Petrie’s measuring work on Cheops Pyramid as genuine. See CHEOPS SOURCES with some excerpts to underline the community.

EQUALITIES: Compiled 25Jan2020 — CRATLAS0 — detailed sections ¦ CRATLAS1 — OVERVIEW ¦ CRATLAS2 — The B¦D¦PG POINTS detailed ¦ MultipleR

DETAILED EQUIVALENTS

EQUALITIES

rJCIRCLE-COMPLEX CALCULATED EXACT QUANTITIES WITHIN THE PETRIE GIVEN MEASURED TOLERANCES

Cheops Pyramid versus Cheops Rectangle from the Golden Section paragon geometrical mathematics based onThe rJCIRCLE

Queen:

THE INNER DESIGN OF THE PETRIE MEASURED CHEOPS PYRAMID IN rJ EQUIVALENTS

Beginning (BackGround) from the so called Queen’s Chamber:

QUEEN’s CHAMBER

See also part of the below in IntroEX — R = [√5 — 1]/2 ¦ b1 = rJCR¦b16 = 4555.88’’:

rJCalc: A = 1790R — hOFFSET ¦ B = A — 97R ¦ C = b1/2√5 ¦ D = 1350R ¦ BD = 254R + hOFFSET ¦ AD = R[97+254] + hOFFSET ¦ EF = 333R ¦ FG = ¦ b1/21 ¦ J = 1350R + π·[5·18 + 16]/5 ¦ H = J — 75R ¦

— »The Egyptian working crew must have been psychic». MustBuyBook.

— ’Scuse me: Several Tight Nominal fits around 0.005 inches is definitely no coincidence.

QUEEN’s CHAMBER:

PetrieNOM.B: ........... (PetrieCH7.40tab¦D=834.4) + (PetrieCH7.41¦BD=184.47);

PetrieNOM.AD: ........ (PetrieNOM.B=1018.87) – (PetrieCH7.40tab¦D=834.4);

AS SEEN: ALL APPROVED EQUALITIES

Lead/Suggestion: AS CONSTRUCTORS aiming at a SIMPLE, not too hard, to deduce plan for the whole construct, we would restrict our choices to a narrow set of CONNECTING CONSTANTS, thereby certifying/strengthening any deductive approach. Such restricted constants or numbers in this complex are

5—GoldenSection ¦ 18—CheopsRectangleNuclearConnector ¦ 16—PyramidAgentNumber ¦ π ¦ R ¦ type R(n+18²)

— These appear recurrently in the construct quantities as exemplified in the links. See also MultipleR examples.

In EXPLICIT for the numbers 18¦58: see MiUNIT: 1’’ = 0.0254 M = R^18·PyramidSquareBase/100R 2decRound;

2 × (PetrieCR¦b58=4534.20 OR PetrieCP¦4534.40) · R^17 = (2.53945.. OR 2.53956.. ) ~ 2.54.

— Both apply.

King:

KING’s CHAMBER

THE INNER DESIGN OF THE PETRIE MEASURED CHEOPS PYRAMID IN rJ EQUIVALENTS

COMPARING EQUIVALENT PETRIE FIGURES WITH The CALCULATED rJCIRCLE COMPLEX QUANTITIES

The OK cell code: IF Difference >Tolerance THEN print ”notOK” else print ”OK”. OK means: approved. NoProblemo.

In general (Quote), Petrie certifies that the Gallery roof top is quite unexplored due to its inconvenient and narrow allowing inspecting space (hazardous height [8.6 M] for any normal pedestrian without specialized security arrangements).

THE GALLERY ROOF TOP SLABS

— Petrie gives though some vital clues to a first rough understanding of the construct at site, illustration below right:

KING’s CHAMBER+: EqualitiesKING

Special Links: S=MiUNIT ¦ PetriePG ¦ First Observation ¦ KingWidth ¦

AS SEEN: ALL APPROVED EQUALITIES

Petrie mentions in PETRIE618 the Great Step value ”61.8±.8¦9” 5 times. We are

— hence, even with a much smaller tolerance (± 0.1) and rounded with 2 decimals

— clearly allowed to adopt a safe and convenient Golden Section

100R = 61.80’’ Petrie Measuring APPEARING CHEOPS RECTANGLE MiUNIT, for further test.

THE GALLERY ROOF TOP:

— Petrie’s figures

”14.5 from the S. wall; the next slab is 47.4 from N. to S”

(PetrieCH7.46 In Quote specifies no roof top tolerances, and no further details are known here on that site)

give a possibly tight fit (± 0.1’’) with two MiUNIT coherent candidates:

• 14.4 modified from Petrie’s 14.5, summed up with 47.4 gives exactly 61.8 = 100R.

— The Petrie mentioned 7 LAPS from Gallery roof top down to the Pyramid S. wall then evenly counts as

14.4 = 7 · 1000/(3 · 9 · 18 + 1/9) = 7000/(486 + 1/9) ¦ 14.4 + 47.4 = 61.80;

• 14.5 with modified 47.3 gives the same Cheops MiUNIT 61.8 with an even 7 resolution

14.5 = 58/4 = 7 · (2 + 1/14) ¦ 14.5 + 47.3 = 61.80;

The PetriePLATE.9 drawing in comparison (above right: magnified from the @Internet Source original) shows a fair resemblance. But no further related data on this part is known here.

See further on THE GALLERY POINT ¦ THE GALLERY TOP.

CheopsATLASintro: MP1: Compiled 19Feb2020 ¦ PART 2 ¦ PART0

CHEOPS PYRAMID CONSTRUCTION PLAN DETAILS SETTLED by rJCIRCLE Complex — Jan2020

FULLY PETRIE CERTIFIED CALCULATED QUANTITIES

Constructive OVERVIEW WITH LINKS — by order of deduction — PART I ¦ all Pyramid measures in Inches: 1INCH = 0.0254 M.

AT FIRST TO BE OBSERVED WITH 100% CLARITY UNLESS ALREADY FAMILIAR: The NUMBER 18. We are dealing with a connection of which modern academy scholars have no idea: TNED deducing — not inventing — nuclear physics through natural constants — The rJCIRCLE connection:

— The Neutron Square — atomic masses = experimentally measured [HOP] — is completely unknown to modern academy. And it will never be adopted either: modern academy ideas of nuclear physics IS a primitive — Provable in every atomic detail, or not at all. Faulty statements are not allowed here. This writ focuses 100% on that statement.

ab:

With all the general data known of The Great Pyramid CHEOPS PYRAMID from Flinders Petrie 1883, we see a beginning from the absolute most simple (a: The GS-body):

— The Most (a) obvious GS-body visual FIT generates (b) a foundational ArcTan½ construction line of 7 fundamental KLMGHBA xy COORDINATE points. 6 of them certifies the genuineness of the 7th casing ENTER point (A) by intersection math calculus by check and cross check reckoning. This is the foundational construct line.

— From the notified Cheops Pyramid rJCIRCLE FIT, we use the two pyramid Golden Section agents (b1) rJCR¦b16 and (b2) PetrieCR¦b58 as exact numerical agency quantitative generators to test their values against the Petrie measured: they should DEFINE the Petrie working group results — within the Petrie given tolerances, or not at all.

— Establishing (c) the basic foundational GS-body xy points between ENTER at the casing (A) and subterranean END (G), a first Petrie (P) xy-point definition is found. P is situated (exactly) between the vertical difference (yG–yG’) of given by the two pyramid agents within Petrie’s given tolerances:

— PetrieCH7.36e states: ........ x4228±2?; y1181±1?.

— rJcalc: ................................. x4227.9960057324; y1181.2240228242.

— The ½(yG–yG’) nominal (2.8172301665) difference (The nValue) has an ArcTan½ triangle hypo-side (n√1.25=3.1497590802) close to π=3.1415926.. Taking the suggestion, we adopt the piFORM as a piVersion for n (and report occasionally throughout our results the (discernible) difference between the two (asserting that any of them will do ..).

OW1:

de:

— Namely (d): Simply Summing yA + nValue directly defines the Petrie measured 19thCourse Stone Masonry Floor Level above the Petrie pavement:

— PetrieCH7.35 states : ........ y668.2±0.1.

— rJcalc: ................................. y668.1482038706. (ROUNDED 668.15→668.2). Nominal Difference: 0.052’’.

The details (e) (ENTER) expose the connections.

fg:

The GS-body paragon gives us (f) direct interpreting instructions in how to connect the descending and ascending tunnel parts through their common referring coordinate point (B):

— At first the Petrie measured B-point is rJCIRCLE complex defined:

— PetrieCH7.39¦64tab states: x1517.8±0.3; y172.9±0.2.

— rJcalc: ................................. x1517.7016293661; y172.9045085255. NomDiff: x0.098; y0.0045.

The (f) delicate Two pyramid agent Mutual Function Principle (TOMFIP) — actual physical pyramid and the ideal Cheops Rectangle rJCIRCLE b16 agent — includes an internal bOFFSET value (21.68’’=21.6799079131). It — obviously — functions as a »Construction Sealing Certificate» pushing the rJ-calculated construction values into the final PetrieCR¦b58 agent — featuring the real physical PetrieCP measured edifice, as here described. So to speak:

— No Cheops Pyramid Tourists are allowed to Understand The Construct unless so »enlightened in the basics».

— Most definitely no 1800+ modern academic scholars. Guaranteed excluded.

The B-point (f) complex gives (g) all the summing constants and parts leading directly to the GS-body Cheops Rectangle rJCIRCLE complex definition of the height — thickness — of the PetrieCH6.32 unveiled and so decisive 19th course masonry »pyramidic principle» (PROVING THE PETRIE 19TH FLOOR ARITHMETICS):

— PetrieCH6.32 states: .......... 37.94±0.17.

— PetrieValuesCalc: ............... 37.9640590055.

— rJcalc: ................................. 37.9657350065. DecDiff: 0.0017.

These coherences prove the affinity details between the actual physical building and the Golden Section paragon CHEOPS RECTANGLE structural plan.

CheopsATLASintro: MP2: Compiled 19Feb2020 ¦ PART1 ¦ PART0

CHEOPS PYRAMID CONSTRUCTION PLAN DETAILS SETTLED by rJCIRCLE Complex

FULLY PETRIE CERTIFIED CALCULATED QUANTITIES

Constructive OVERVIEW WITH LINKS — by order of deduction — PART II ¦ all Pyramid measures in Inches: 1 INCH = 0.0254 M.

THE B¦D¦PG POINTS.

WITH The full corresponding Petrie measured Cheops Pyramid Golden Section CHEOPS RECTANGLE B-point determination from the two pyramid agents rJCR¦b16 and PetrieCR¦b58, the crucial sloping top Gallery floor PG point is defined and identified with Petrie’s given values:

— From PetrieCH7.46: .......... 1658.2±0.6.

— rJcalc: ................................. 1658.1652607385. NomDiff: 0.035.

The D point (TP26detailed) between PG and B — the floor level into the Petrie named Queen’s Chamber at the Gallery’s lower north beginning — is rJCIRCLE complex identified with the Petrie (averaged mean) specified values in offsetting the regular direct GS-body FIT as depicted (TP26detailed) in the illustration above:

— From PetrieCH7.39: .......... x2907.3±.6; y852.6±.3.

— rJcalc: ................................. x2907.3786302; y852.8245796. NomDiff: 0.079; 0.225.

on the SIMPLE intersection offset (horizontally contracted) operation

bOFFSET/2 ¦ bOFFSET + 18/2 .......... see full details in TP26.

— See also complementary ways below in Petrie on Queen’s Chamber.

The rJCIRCLE complex Cheops Pyramid inner design Golden Section CHEOPS RECTANGLE construction plan

is exclusively proved in this clear cut obvious quantitative precise Petrie precision TRANSPOSED connection:

TransPond: — yKINGgallery THE TRANSPOSITIONS

This is also some real steel: parameters connecting begin and end of the ascending tunnel:

20Feb2020. Discovered transposition equivalent: RECURRING QUANTITIES exposes A Construction plan: B point to Gallery PG point.

——————————————————————————————————

yATH ¦ BUARM ¦ yBlimit ¦ yPonB ¦ Fangle ¦ yBarm

Same rJCIRCLE complex CONSTRUCTION PLAN parameters reused.

The rJCIRCLE complex calculated B-point parameters transposed onto the top sloping Gallery floor, obviously defines the Petrie given figures with some high measure of tightness:

King’s Chamber PetrieCH7.46, floor level:

yKINGPetriePG: ....... 1693.2 ± 0.6:

yKINGrJcalc: ............. 1693.1782168993. NomDiff: 0.022 as follows:

+ yPG ......................... = 1658.1652607385

+ yBlimit ..................... = 4.1112567233

+ S/2 ........................... = 50R = 30.90169944 = 1693.1782168993.

The yBlimit+50R is mentioned by PetrieCH7.46 (”34.92 or 35.0 on E”) as the Step Face height: = 35.0129561608.

Further examinations on whole number R-multiples also give other alternatives in approving on Petrie correspondences within his given tolerances.

— See more examples on King’s and Queen’s Chambers in Multiple R Values.

KING’s MIDDLE:

King Chambers Mid-point from pyramid vertical midpoint:

KCM¦PetrieMean: ................ 433.8±0.8.

rJcalc with multiple already defined and used parameters:

KCM¦rJ: ................................ 433.6963998752 = 10yATH;

KCM¦rJ: ................................ 433.5981582616 = 20bOFFSET; yATH/bOFFSET = 2.0004531459.

— Both rJ¦KCM lie within Petrie’s given tolerance.

We have no here known arguments to exclude these as intended from an advanced construction plan.

The two chambers widths and lengths also approve from rJcalc on multiple R:s within the Petrie given tolerances as follows;

Petrie on King’s Chamber:

The final collapse is approaching — the condition of the building around 1883, King’s Chamber

”.. especially as it must be remembered that this shows its actual state, and not precisely its original form.

On every side the joints of the stones have separated, and the whole chamber is shaken larger. ..

These openings or cracks are but the milder signs of the great injury that the whole chamber has sustained, probably by an earthquake, when every roof beam was broken across near the South side; and since which the whole of the granite ceiling (weighing some 400 tons), is upheld solely by sticking and thrusting.

Not only has this wreck overtaken the chamber itself, but in every one of the spaces above it are the massive roof-beams either cracked across or torn out of the wall, more or less, at the South side; and the great Eastern and Western walls of limestone, between, and independent of which, the whole of these construction chambers are built, have sunk bodily.

All these motions are yet but small—only a matter of an inch or two—but enough to wreck the theoretical strength and stability of these chambers, and to make their downfall a mere question of time and earthquakes.”, PetrieCH7.51e.

” The position of the King’s Chamber in the Pyramid is defined thus: N. wall at base

330.6 ± .8 S. of centre of pyramid; S. wall

537.0 ± .8 from centre; E. wall [corrected error] =

305.1 ± 3.0 E. of centre; W wall

107.7 ± 3.0 W of centre. .. ”, PetrieCH7.55.

• (537.0 + 330.6)/2 = 433.8 ± 0.8 ................... chamber midway distance from centre;

• 537.0 – 330.6 = 206.4 ± (0.4) ....................... SouthNorth chamber width

• 305.1 + 107.7 = 412.8 ± (3) ......................... EastWest chamber length

— But PetrieCH7.51 also states

” For example, the N. wall is on average 412.59 inches long”.

PetrieCH7.52Tab gives a TopMeanBase-table with

NS-values ranging 411.88→412.78 (diff.: 0.90) and

EW-values ranging 205.97→206.43 (diff.: 0.46).

— With Petrie’s chamber conditions in quote, the original (very) precise measure is obviously disrupted ”only a matter of an inch or two”, making every precise comparison (here) out of the question; Speculations (here) are not allowed. Especially not in terms of stated tolerances in the range of 3 inches.

— A rJ examination of the ± 0.4 tolerance 206.4 inch value for comparison shows:

KING WIDTH South→North

KW¦PetrieCH7.51Mean: .................... 206.4±(0.4).

KW¦rJ: ................................................ 206.4233522425. Diff: 0.023;

KW¦rJ = R(10+18²) = 206.4233522425.

The corresponding King’s Chamber EastWest length is, as quoted, clearly corrupted by its huge stated tolerance (±3.0’’). In his CH7.52 table, Petrie gives us (at best) a South wall value of 412.11 inches for rJ comparison:

KING LENGTH West→East

KL¦PetrieCH7.51¦52: .......................... 412.11 (earth quake corrupted as quoted, uncertain value).

KL¦rJ: ................................................ 412.1996887244. Diff: 0.090;

KL¦rJ = (PetrieCR¦b58 = 4534.1965759686)/11 = 412.1996887244.

— No doubt there is some Basic Construct Plan going on here ..

We test for the same route on the Queen’s Chamber:

Petrie on Queen’s Chamber:

” In the Queen’s Chamber it seems, from the foregoing statement that the ridge of the roof is exactly in the mid-place of the pyramid, equidistant from N. and S. sides; it only varies from this plane by a less amount than the probable error of the determination.

The size of the chamber (after allowing suitably for the incrustation of salt) is on an average

205.85 wide and

226.47 long,

184.47 high on N. and S. walls, and

245.1 high to the top of the roof ridge on E. and W. walls. ..”, PetrieCH7.41.

In a following table Petrie gives tolerance values ranging –0.17→+0.29 for the South-North width (we adopt a rough worst case ±0.10), and –0.50→+0.56 for the East-West length (we adopt ±0.50 but will use only ±0.30):

QUEEN WIDTH South→North

QW¦PetrieCH7.41: .......................... 205.85(±0.10).

QW¦rJ: ................................................ 205.8053182537. Diff: 0.045;

QW¦rJ = R(9+18²) = 205.8053182537.

QUEEN LENGTH West→East

QW¦PetrieCH7.41: .......................... 226.47(±0.50).

QW¦rJ: ................................................ 226.7098287984. Diff: 0.24;

QW¦rJ = (PetrieCR¦b58 = 4534.1965759686)/20 = 226.7098287984.

Type18:

In both pairing cases

KING WIDTH South→North

KING LENGTH West→East

and

QUEEN WIDTH South→North

QUEEN LENGTH West→East

the rJCIRCLE complex apparently uses exactly the same calculating method:

R(10or9+18²)

(PetrieCR¦b58 = 4534.1965759686)/11or20

to gain the results.

— That obviously associates a very strong connection to A PRINCIPAL PRINCIPLE EXISTENCE OF a foundational plan: precise advanced constructiveness. We don’t know (yet) from where, only that it is standing there.

— No doubt: The search for an answer IS a very exciting expedition: — »Will we ever find it? How did it go? Was it shiny?».

Another Queen site value in a simple Number18 coherence:

With further Petrie Queen Chamber values (the site is partly rough and uneven), the roof top (245.1’’) from the floor level (834.9’’) measures precisely

1080’’: 834.9 + 245.1 = 1080;

— That is also exactly the product of 60 and 18:

60 · 18 = 1080.

QUEENspecial:

QUEEN SPECIAL

Specifically for the QUEEN FLOOR LEVEL yQUEEN contra the KING FLOOR LEVEL yKING, and the rJCIRCLE complex transition parts already used (even closer that the yQUEEN multi R-alternative):

THE QUEEN CHAMBER LEVEL ABOVE THE PETRIE PAVEMENT

Compare the direct GS-body alternative in The Petrie D-Point.

PetrieCH7.40tab: ”856.2 ±.3 ¦On floor”;

Petrie yQUEEN: .................... 856.2 ±.3

rJcalc: .................................... 856.2949417436. NomDiff: 0.095;

yQUEEN = yKING/2 + bOFFSET – 18 + 2yConB = 856.2949417436 ~ 856.3:

(1693.1782168993)/2 + 21.6799079131 – 18 + 2(3.0129626904) = 856.2949417436.

The bOFFSET – 18 part in explicit (it also connects to the yPonB part) is the horizontally contracted result of which vertical (ADD1.84) ArcTan½ spouse marks the casing spotting limit (The Petrie available visual space between 1 and 4) from the actual physical floor descending passage construction:

The details — the FIT in the edifice — are somewhat and sometimes so amazingly astonishing that one sometimes wonder if these quantities and numbers with their figures, really, are real or just a magic dream. Those who made it really had a feeling for it.

the physical possibility along the descending entrance passage of finding the actual Petrie measured casing spot (pA) connecting The 19th course floor level. See details from ENTER unless already acquainted.

What is known here:

— The above exemplified coherences makes it impossible to reject »The Plan» as ”a mere coincidence”.

— It — the rJCIRCLE Golden Section Paragon CHEOPS RECTANGLE geometry — is obviously an integrated detailed description of the whole edifice as The Great Cheops Pyramid.

HollowAspects:

The Great Cheops Pyramid

WHY THE HOLLOW CONSTRUCTIONS — ”air shafts”, ”ramp holes”?

— The inner core masonry has, apart from the tunnel systems some additional ”air shaft channels” and specifically in the Great Gallery sloping floor ramp along its side, some peculiar rectangular hollow vertical details of unknown function.

— What’sUp?

PetrieCH7.41 (Queen’s Chamber) mentions measurement influence from

”incrustation of salts” and CH7.43 ”salt exudation”.

These are obviously long time effects (thousands of years depending on climate conditions).

Apart from a possible sophisticated »ventilation system» (reducing chemical attacks on the tunnel walls during long periods of time), the ramp issue may have some alternative explanation. See THE OTHER HOLES.

Advanced engineering.

CheopsATLASmain: MP0: Compiled Jan2020 — PART1 ¦ PART2

CHEOPS PYRAMID CONSTRUCTION PLAN DETAILS by rJCIRCLE Complex

FULLY PETRIE CERTIFIED CALCULATED QUANTITIES

Constructive OVERVIEW QUANTITIES WITH LINKS — by order of deduction — PART III

Not much in this presentations seems to be known in modern quarters.

— The Golden Section Paragon Body forms the unique bd=h² triangle or pyramid section here coined CHEOPS RECTANGLE:

GOLDEN SECTION EDIFICE — how the unique bd=h² pyramid triangle appears:

Through TNED observations from the rJCIRCLE which envelopes the GS paragon Cheops Rectangle body, a seemingly very precise layout structure coherently appears from the 1883 Flinders Petrie group measured CHEOPS PYRAMID:

MODERN ACADEMY IS CHALLENGED by the simple GS-paragon body fits on The Cheops Pyramid edificial design:

Investigating the apparent CHEOPS PYRAMID¦rJCIRCLE¦GS-body coherency, simple and straight quantitative matches show up — from a basic The 7 Points xy coordinate set through the GS paragon’s ArcTan½! Line. We will see and study how the general whole of the Cheops Pyramid construct is explained in detail on lengths and angles from this coherent fit — in perfect match with Petrie’s given values and their specified tolerances. The compilation below has links to the more detailed actual describing sections, unless already familiar.

R = (5^½ — 1)/2 Point A: FULLY PETRIE CERTIFIED CALCULATED QUANTITIES

unitINCHES rJCR internally calculated formula/term

——————————— ————

Tunnels 26° 33’ 54.18’’ A° = ArcTan½

CASING Angle 51° 49’ 38.25’’ C° = ArcCot R^½

nValue 2.817¦2.8172301665’’ (yG — yG’)/2 = (1184.04 — 1178.41)/2 = 5.63/2 = 2.815’’

FULL DECIMALS: 1184.0412529906 — 1178.4067926577 = 2.8172301665’’

yA 665.34¦665.3382779782 GS 7

19thFLOOR y 668.15¦668.1482038706 yA+n

xA 523.06¦523.0566039073 GS 7

unitINCHES PETRIE MEASURED/calculated rJCR calculated Petrie formula/term

——————————————— ——————————— ————

CASING Angle PetrieCH6.24¦32 51° 53’ 20’’ ± 1’ not (fully) connected PETRIE°* ROOF18 ¦ Petrie’s19th ¦ ENTER

19thFLOOR y 668.20 ± 0.10 668.15¦668.1482038706 yA+nValue

yA 668.20 ± 0.10¦PetrieCH7.36 668.15¦668.1482038706 yA+nValue

xA 524.10 ± 0.30¦PetrieCH7.36 524.10¦524.1043769892 (yA + nValue)/tanPETRIE°

* Erosion/earthquakes by time and attacks from treasure hunters affect future variations on Petrie’s Casing Angle

R = (5^½ — 1)/2 Point B: by deductive order: see The G-point first

unitINCHES PETRIE MEASURED/calculated rJCR calculated Petrie formula/term*

——————————————— ——————————— ————

yA 172.90 ± 0.20¦PetrieCH7.64tab 172.91¦172.9045085255 yB — (yBlimit = yConB + SIO)

xA 1517.80 ± 0.30¦PetrieCH7.64tab 1517.70¦1517.7016293661 xB + 18

* yConB = yPangle@H-end + yHangle@B-end = 3.0124757861’’

SIO = yConBoffset = nValue — D

The D part is the dValue-projection into a xyA-vertical;

The dValue is trigonometrically calculated from the floor construction offsets — from the G-point:.

R = (5^½ — 1)/2 Point G:

unitINCHES PETRIE MEASURED/calculated rJCR calculated Petrie formula/term

——————————————— ——————————— ————

xP 4228 ± 2 ?¦PetrieCH7.36e 4228.00¦4227.9960057324 xG + 10R

yP 1181 ± 1 ?¦PetrieCH7.36e 1181.22¦1181.2240228242 yG — nValue = yG’ + nValue

1181.23¦1181.2313270982 The pi-version, also below:

The P°Angle 26° 31’ 23’’ ± 5’’ ?¦PetrieCH7.36e 26° 31’ 17.48’’¦(26° 31’ 18’’)? 26° 31’ 17.486086’’ *ForCA

lowest ?: 26° 31’ 18’’ APPROVED only with Petrie’s Question Mark

The H°Angle 26° 29’ ± 1’¦PetrieCH6.32e 26° 29’¦26° 28’ 58.55’’ Hangle*

* piVersions:

Pangle = ArcTan½ – ArcTan(π/[AGdistance=4135.338346’’])

Hangle = ArcTan½ — ArcTan(dValue/2yA(1,25)^½)

R = (5^½ — 1)/2 Point D:

unitINCHES PETRIE MEASURED/calculated rJCR calculated Petrie formula/term

——————————————— ——————————— ————

xP 2907.30 ± 0.60¦PetrieCH7.39 2907.38¦2907.3786302 *

yP 852.60 ± 0.30¦PetrieCH7.39 852.82¦852.8245796 *see also Queen Chamber Series

* Specific Simple GS-body paragon intersections with xLoAnom + bO/2 and xLoBnom + bO + 18/2

XLoBnom = LowerBlineNOM ....... =

XLoAnom = LowerAlineNOM ...... = b — P

xyAB = intersection point from LineAB, see Intersection Math unless already familiar.

THE D-ANGLES by deductive order: see The PG-point first — R = (5^½ — 1)/2

unitINCHES PETRIE MEASURED/calculated rJCR calculated Petrie formula/term

——————————————— ——————————— ————

(B’.pG)° 26° 12’ 50’’¦PetrieCH7.39¦46 26° 12’ 51’’¦26° 12’ 51.16 95 06’’ *ARCTAN (2683R - 280R)/(F4 - 2456R)

* ARCTAN (1658.2 - 172.9)/(4534.4 - 1517.8);

Petrie gives no tolerance. He states s39:

” This, when corrected for lower signal being 3 too high, gives

26° 12' 50" for mean angle of both passage and gallery together.”, and in s46:

”.. the step will be

61.1 long; and this at the angle

26° 12' 50" (by which the end of the gallery was calculated from the plug-blocks) will be

30.08 vertically ..”.

(B’.D)° 26° 2’ 30’’¦PetrieCH7.38¦39 26° 4’ 31’’¦26° 4’ 31,22 09 20’’ *ARCTAN [yD—yB-yBlimit]/[xD—xB—18]

* ARCTAN (852.6 - 172.9)/(2907.3 - 1517.8)

26° 3’ 59.17 05 23’’ — Petrie gives no tolerance:

— PetrieCH7.38 gives several different angular values over the path B’.D ranging from 26° 2’ to 26° 7’. And he states:

” .. it will suffice to say here that the mean angle is 26° 2' 30" ”.

Trigonometric cross checking with Petrie’s own specified lengths show some [minor] deviations, [still within the Petrie given tolerances].

(D.pG)° 26° 20’ 26’’¦PetrieCH7.38¦PetrieDangles 26° 20’ 1’’¦26° 20’ 0.43 27 59’’ *ARCTAN (yPG - 1380R)/(F4 - 4704R)

* Never mentioned by Petrie. See TP27.

— Petrie cogitates a section of arguments without mentioning the actual [measured] angle. PetrieCH7.39:

” Hence we cannot say exactly what direct relation the theodolite bore to the passage;

but we can obtain the angle of slope very satisfactorily, by taking ..”.

— With the Petrie given length we can cross check-calculate the missing part as described in TP27.

*See SCHEMATIC OVERVIEW and WHOLE NUMBER R MULTIPLES

F4 = PetrieCR¦b58 = 4534.1965759686’’ ¦ 4534.20’’ — PetrieCP¦bLOWEST = 4534,15’’

— Because the B-PG ascending construction line from The rJCR¦b16 Agent original has no actual physical representation in the edifice — see from The Push — The Petrie B point [B’] — a FLOOR preference — takes the actual physical construct reference. In order, as here so understood, to secure a clear measuring sight line up to the Gallery south end on that construct, the sloping Gallery Ramp floor must have a small BREACH guaranteeing that no material covers a measuring sight line. This condition means, InPetrieQuote Col2 Row23, a slight BENDING at the D-point between the two parts upper-lower along the ascending path: One smaller angle B’D, and one larger angle D.pG with the mean on the whole path as B’.pG.

— But Petrie — in part: TP27 gives a full account — leaves out some measuring data [on D.pG] which forces us to »recalculate AND CHECK Petrie’s presented [angular] values» — with some minor but still acceptable deviations within the Petrie given tolerances: no big deal.

— As we already have calculated the basic reference points from the rJCIRCLE agents as The Petrie D-point [LinD], The Petrie B-point [LinB] and The PG-point [LinPG], these angular comparing calculations — here — can use a more convenient grip: Whole Number R-Multiples — where these lie within the Petrie given measures and their tolerances — simplify the comparing angular values process.

— Petrie gives no direct trigonometric formula for the angularly calculated results. So we just have to ”fill in” with the most simple of the Petrie given values, lengths, to check and cross-check the valid results.

— The full account for these calculations are given in the section TP27.

R = (5^½ — 1)/2 Point PG:

unitINCHES PETRIE MEASURED/calculated rJCR calculated Petrie formula/term

——————————————— ——————————— ————

yP 1658.20 ± 0.60¦PetrieCH7.46 1658.17¦1658.1652607385 [b1 — xB]/2 + yB — [ yATH + BUARM]

xP 4534.40± 0.25¦PetrieCH7.25 4555.88¦4555.8764838817 *b1 = rJCR¦b16

* SEE THE SEALING PUSH: The rJCR¦b16 agent’s calculated yP value through its b=4555.88’’ is just hung on the PetrieCR¦b58 agent:

— The rJCR¦b16 agent is so only USED to generate this yB-value — which origin effectively is hidden below bhOFFSET the Petrie pavement of the regular Petrie Cheops Pyramid agent PetrieCR¦b58 = 4534.20’’. Unless familiar with the two geometrical ideal pyramid agents, nobody will — ever — understand The Construction Plan: it will be a complete enigma until revealed through the [»most simple»] rJCIRCLE complex.

PetrieCR: FigureCASINGS ¦ The TouristVersion ¦

COMPILED FOR UNIVERSE HISTORY 3Feb2020 — The full Mathematical and Geometrical disclosure — ATLAS — of The Great Cheops Pyramid from The 1883 measures by the Flinders Petrie working group.

Compiled short overview with links included to the actual detailing sections

RELATED MATHEMATICS AND PHYSICS — FROM THE BEGINNING

HOW TNED EXPLAINS THE 1883 FLINDERS PETRIE MEASURED CHEOPS PYRAMID

Begin — CHEOPS RECTANGLE:

Who built the fit?

With the mathematical geometry thoroughly defined for the Golden Section paragon (the GS-body), and The 1883 Flinders Petrie measured Great Cheops Pyramid, as observed by the TNED rJCIRCLE, a first seemingly exact fit appears between the two through The ArcTan½-line:

———————————————————

ENTER ¦ GS-body — HOW IT ALL STARTED — PHASE 1 — THE CONSTRUCT FOUNDATION LINE

The 7 fundamental coordinate points K L M G H B A along the entrance sloping ArcTan½ line are determined for further exact Petrie measured quantitative comparing.

All calculations in this presentation are given through the main pyramid agent rJCR¦b16 with some support from the ideal PetrieCR¦b58 agent.

— All vertical height values are related to the Petrie given pavement.

The rJ-reference certifies — once and for all — that no possible tracing to the origin will be possible UNLESS (correspondingly) TNED familiar: The rJCIRCLE is the guide.

Concealed Construct: PetrieCR ¦ HowStart

A Concealed Construction Plan — See pyramid agent details in Introduction

— The two Pyramid Agents CR and rJ with the actual remaining Cheops Pyramid (CP):

— The actual construction plan quantities — however — is made from the rJ part relative the CP¦CR part so:

— All ideal INNER DESIGN GS-body Cheops Rectangle (CR) EXACT numerical quantities — the whole plan — are reckoned with the rJ part’s baseline on the Petrie pavement. Same vertical height reference as our two pyramid agents CP and CR.

Because the whole geometrical design builds on two differently sized but perfectly uniform pyramid agents, the design layout can freely dispose of either agent to GENERATE EXACT QUANTITIES. In finalizing this layout, both pyramids share the same casing and top, but have slightly different bases and heights: the larger rJCR¦b16 agent has its base 27.58’’ below the Petrie pavement with a 2×21.67’’ broader base. The resulting original layout so becomes SEALED, projected finally only on the visual PetrieCR¦b58 agent, corresponding to the Petrie measured PetrieCP Cheops Pyramid.

— Nobody will even come close to even a clue to the original construction plan unless acquainted with the rJCIRCLE part [as in TNED].

The seal is realized by pushing [schematically as illustrated] the CR-part into the rJ-part with the horizontal half pyramid base offset difference (21.68’’) between them. All acquired values then become safely hidden from any direct inspection — until someone enough motivated to dig, deep [nuclear physics stuff, see from NatCH], discovers the plan.

Finally, with the rJ pyramid agent’s baseline level situated (27.58’’) below the Petrie pavement, both pyramid agents rJ and CR now share one and the a same original Cheops Pyramid top and casing.

All pyramid data is then lying transposed onto the only visual remaining pyramid agent CR. It will be impossible to discern as separate from the actual Cheops Pyramid edifice — as measured by Flinders Petrie and his given tolerances.

Both CR and rJ agents have exactly the same casing and top. The only difference is that rJ have a lower baseline — and the whole construct plan is safely sealed inside the two — as one — as described.

SPECIFICALLY:

The entrance point A — reckoned from the rJ agent — is/becomes directly transposed ONTO the actual built Cheops Pyramid PetrieCR¦b58 pyramid agent.

Nobody will have the slightest clue, unless rJ acquainted. It will be a concealed riddle.

See also Petrie references [PetrieCH6.22] of the lower casing socket measures in IntroTEFF

[all four corners with different vertical ground socket sets between 23-40’’ below Petrie’s pavement].

Such an edificial planning obviously needs some real steel sophisticated tools.

See detailed IntroEX quantity examples from QUEEN’s CHAMBER: How the rJCIRCLE Golden Section Cheops Rectangle complex forms the Cheops Pyramid basics within the Petrie given values and their tolerances.

The description continues from there with overviews and detailed descriptions of the different sections, and how they are calculated in their approved quantity equivalence with the Petrie given measured values.

The rJCIRCLE complex is explained from the beginning from NatCH.

— All section after explain the different details.

Summation:

Summation

In all (4Feb2020):

— The GS-paragon Cheops Rectangle specified as the main constructive pyramid agent rJCR¦b16 determines provably by quantities the corresponding measures specified by the Flinders Petrie working group in his 1883: The geodesically measured The Great Cheops Pyramid. The corresponding quantities prove the connection.

IntroTEF: PetrieCR — An introduction to

HOW TNED is connected to THE 1883 FLINDERS PETRIE MEASURED CHEOPS PYRAMID

Introduction — see also further Petrie data At the built precision

DETAILS ON THE OUTER FORM

SOME BASIC DETAILS ON THE OUTER FORM OF THE GREAT CHEOPS PYRAMID SHOULD BE FAMILIAR;

SCHEMATICALLY:

— The leftmost below schematically iconic drawn figures

represent the only remaining ”The Cheops Tourist Version”

that is left for us to visit:

remnants of The Great (ancient named Greek Cheops) Pyramid.

TheTouristVersion:

PetriePLATE.11 shows a drawing of the pyramid’s ”CASING-STONE IN AVERAGE CORNER SOCKET”, partly iconized below.

— The term here ”casing overlay” refers to the vertical and upwards additional masonry over the remaining casing stones that we safely can assume once were. Documents tell about the great earthquake period in Egypt (late 1100) after which the casing part of the Cheops Pyramid masonry was removed to rebuild Cairo.

The unevenness with partly eroded end blocks in the pyramid staircase masonry gives no direct precise information of the vertical casing overlay metrics (roughly 1.6 M from PetriePLATE.9).

No other known specification of this parameter has been found in Petrie’s work from 1883 on The Great Pyramid. Or that such information exists, but is not directly easily recovered.

— The remaining casing blocks (PetrieCH6.29, ”.. the remaining casing stones on the N. base”) are said to be of order ”few”.

— With some help of further photographic documents @Internet 26Dec2019, they seem to be situated on the Pyramid’s North mid side, below the pyramid entrance. (All other remnants of these casing stones, if any on the other pyramid sides, are badly eroded).

— Base and Angle. That is the outer formative basics reported from Flinders Petrie (1883).

— Our comparing agent is The Golden Section — the ideal simple Cheops Rectangle Geometry.

As is stated by Flinders Petrie (PetrieCH6.24) ;

— The average measured value 51°52’ ± 2’ of the sloping angle of the remaining pyramid walls was taken (preferentially) from the north side measurements along the slope of the pyramid’s remaining — partly eroded staircase masonry. (The eroded parts makes a more precise [small scale] measure out of the question).

FIGUREcasings: ICONIC

THE CASING ORIGINAL

Figure b: The ”Tourist Version”;

— Pyramid staircase masonry. Partly in bad shape, with a few remaining casing stones at the north side of the pyramid base. The average slope value specified by PetrieCH6.25 of the remaining staircase masonry is

51° 52’.

— For the vertical and upwards casing overlay, we only have a relative value based on a PetriePLATE.9 drawing showing approximately

1.5(59’’)-1.6(63’’) M at the base.

Figure c: The TouristVersion’s actual Petrie measured version.

— This is the actual Cheops Pyramid we find in the Flinders Petrie based measures.

Figure a: Petrie’s Pyramid base in figures bc taken directly on the Petrie partly, see PetrieCH6.24, measured casing stone slope value

51°49’.

— It is practically identical with The Golden Section and Cheops Rectangle slope value angle

C° = 51°49’ 38,2525’’ = ArcTan (h/b = 1/√[R=(–1+√5)/2]) = 51.82 729 237°. Also in PREFIXxSIN: ArcSin R = C°.

— However: No definite direct Petrie given such value exists — presumably partly due to uncertainty issues on only the few remaining casing blocks (also partly ”owing to irregularities”).

— The figure a-type then, will be our only possible EXACT GEOMETRICAL candidate in any explaining ATTEMPT of the whole Cheops Pyramid complex — from the TNED point of view: the actually obtained rJCIRCLE and its claim of enveloping the whole Golden Section Construct.

Figure d: The actual rJCR¦b16 Pyramid Agent;

— Just the vertical — 27.58’’ below Petrie’s Pavement — elongation of a:

It is the rJCIRCLE¦b16 CONSTRUCTION version — here to be tested.

NatCH: Continued Description ¦ The Device

(Sw.ed. CUV-analysen CHEOPSPYRAMIDEN UTMANAR VETENSKAPSSAMFUNDET)

The rJCIRCLE Complex — OVERVIEW in short: See INTRODUCTION

NATURE CHALLENGES MODERN ACADEMY (1800+)

— says TNED. We examine the statement. In deep.

TheDevice:

NATURE CHALLENGES MODERN ACADEMY

THE CHEOPS RECTANGLE — From Mathematics 5 basic Laws — The Cheops Pyramid (Petrie 1883)

The Cheops Pyramid Paragon from The Golden Section — by exact Geometrical Mathematics:

See also unless already familiar GOLDEN SECTION ARITHMETICS

GOLDEN SECTION EDIFICE — how the unique bd=h² pyramid triangle appears:

The Golden Section constant R=(√5 –1)/2 with its paragon-morphological geometry shows us directly where any significant intersections appear in the corresponding geometrically unique Cheops Rectangle bd=h² triangle; Its tangent and slope

ArcTan[h/b=√(2/[–1+√5])=1,27201965]=51.82729238° = 51°49’38.25’’. With a transparent overlayed section as seen from above along with a ground spotting westerly view ahead as seen from the rising sunny east side, the center of the construct appears as the Cheops Pyramid in illustration above:

— All thorough dimensions here are derived from Flinders Petrie Sources @Internet in his (1881-1883) measuring works on the same so called The Great (ancient Greek: Cheops) Pyramid. Precise data with quotes from Petrie will be frequently referred to in this presentation.

HowStart:

How it all started — basic geometry illustrated

— Just a simple innocent test that suddenly

— Wao. Is that really so, simple?

brightened up on its surprisingly simple direct result:

— GS-R = (√5 – 1)/2 = 0.618033988..; (rJ[mJ=5.975T24KG]=7817.80’’)/100R = √16000.9..; (PetrieCP¦b=4534.40±0.25)’’/rJ = 0.58000..

FOUND STUFF. Faulty statements are not allowed here.

FIRST BASIC: rJ = 198.5721548 M = 7817.80’’ — See constants in HOP.

Adopted more precise mJ value from the ideal rJCR¦b16 value 4555.88’’:

mJ = 5.9744931448 T24 KG from rJ = 198.5665397062 M = 7817.5803033942’’

CENTRAL CONSTANTS: u, m(n), m(e), h, c₀ as given from the Instrumental Epoch (IE 1960-1999) HOP section.

The rJ-equation expresses the radius of a Dmax compact TNED N3m20 deduced neutron body with the mass of the Earth

mJ=5.975 T24 KG, a sphere with a (Dmax) density of

1.82 T17 KG/M³.

That is a sphere precisely as illustrated NatCH:

— a circle enveloping the d-corners of the Golden Section ¦ Cheops Rectangle:

The rJCIRCLE center/origo is situated in the intersection C¦y.

With PETRIEb=4534.40’’ and rJ=7817.80’’ the relation is

PETRIEb/rJ = 0.580009271

and the relation

rJ/100R = √16000.9049099833.

— That is how it all started: WE BEGAN TESTING THE SIMPLE NUMBERS FOR (ev.) EXACT FITS.

— Testing the precision, we adopt the two ideal Cheops Rectangle (CR) Geometries for

PetrieCR¦b58 .......... 58R√16000 = 4534.196576 ~ 4534.20’’:

— The actual ideal Flinders Petrie Cheops Pyramid with its ideal Cheops Rectangle casing;

IDEAL: rJCR¦16 = 100R√16000 = 7817.580303’’

k0¦GS = √[(0.5+2/√5)²+1] = 1.7159333294 = rJ/b ; b:=rJCR¦ b16=4555.88’’;

rJCR¦b16 ................ rJ/k0 = (100R√16000) / √[(2/√5 + 0.5)²+1] = 4555.876484 ~ 4555.88’’.

— EXACTLY The Same as the b58-pyramid, but with its pyramid base situated slightly below [27.58’’] the Petrie Pavement zero height reference.

Basics as calculated from the rJ-value in NatCH.

PETRIEb ................. 4534.40’’ ± 0.25

The comparing 1883 Flinders Petrie measured Cheops Pyramid’s half base on its determined pavement as the established Petrie zero height reference.

We use the abbreviations

PetrieCP .................. for Petrie given measured values on the Cheops Pyramid (CP)

PetrieCR .................. for corresponding IDEAL Petrie Cheops Rectangle (CR) — GS-body — values

PetrieCR refers the PetrieCR¦b58 value 4534.20’’ while PetrieCP refers

Petrie’s own measured values: 4534.40’’ ± 0.25.

The three following iconic

CHEOPS PYRAMID COMPLEX ILLUSTRATIONS

will help in navigating the (tight) description:

PetrieCP PetrieCheopsPyramid: Petrie measured the average slope of the pyramid staircase masonry as 51° 52’ , with a more narrow particular casing stone slope of 51°49’ on the remaining few stones at the pyramid base;

PetrieCR PetrieCheopsRectangle: With the pyramid’s half side PETRIEb=4534.40’’ ± 0.25 on Petrie’s casing slope, ideally the same as the ideal Cheops Rectangle slope 51°49’ 38.25’’ we obtain a broader and higher top pyramid enveloping Petrie’s staircase’s 51°52’ masonry.
— If we test the 0.58 candidate for this purpose we find a corresponding
PetrieCR¦b58 = 4534.20’’ — well within the given tolerance interval with its lowest 4534.15’’ — with the help of the near rJ-spouse and its ideal EXACT rJ = 100R√16000 = 7817.58’’. And where NOW we have
PetrieCR¦b58 / rJ¦16 = 58/100 giving the new PetrieCR¦b58 = 58R√16000 = 4534.196576’’ ≈ 4534.20’’.

rJ¦CR The enveloping MASTER Cheops Rectangle — exactly the same top as PetrieCR, but lower, beneath the Petrie Pavement with an additional 28.48’’, as calculated separately.

While Petrie’s Cheops measurement have no fix and stable preference except the Petrie measured Cheops Pyramid base (4534.40’’ ± 0.25) and the mean staircase masonry slope (51° 52’ ± 2’), the two new testing envelopes PetrieCR and rJ¦CR do have such properties.

What does that situation suggest?

The situation suggest that IF the pyramid was intended as such, these two solid preference guiders and a marker WILL define a clear reference where Petrie’s measurement WILL coincide — practically excellent perfect — or not at all. That will be our test.

— We have already seen that there (already) is a profound VISUAL fit in the simple geometric paragons. But how close is it, and what can it clarify, and elucidate?

See a Continuing Description after the below describing linked passages.

TheCheopsATLASfoundation:

ALL ABOUT WHAT THE ENTIRE COMPLEX IS FOUNDED ON.

INTRODUCTION: NatCH

Nature challenges MAC

INTRODUCTION TO NatCH — rJCIRCLE Response

A FULL QUANTITATIVE CONSTRUCTION LAYOUT PROOF

Additional basic terms and meanings in HowStart and The GS-body

TwoPagents:

A full quantitative proof has been found/clarified (10Jan2020):

Statement:

A DEDUCTION is asserted to be absolutely EXCLUDED to the inner Cheops Pyramid paragon structural DESIGN

The Golden Section paragon body

Proof:

without the rJCIRCLE Cheops Rectangle as a fixed no tolerance quantitative index by exact geometrical quantities: fractions, roots (pi + natural physical constants [Planck constant]).

bOFFSET: bNOM

»THE CHEOPS RECTANGLE PYRAMID OFFICE» AND ITS

TWO PYRAMID AGENTS — HowSTART

b₁ — b₂ = 21.68’’ = bOFFSET

b1 = [rJCR¦b16 = 100R√(16000/[(2/√5 + 0.5)²+1])] = 4555.876484’’]

b2 = (58R√16000 = 4534.196576’’) The Petrie Cheops Rectangle Pyramid Agent PetrieCR¦b58 = 4534.20’’

b1 — b2 = 21.6799079131’’

2R = √5 — 1

The GS-body paragon is applied on the slightly larger same top rJ Cheops Rectangle rJCR. Its 27.58’’ higher/deeper Cheops Rectangle bd=h² pyramid is then pushed vertically the same 27.58’’ up to the basic pavement Petrie level — and an additional half pyramid base offset 21.68’’ South to North INTO the corresponding ideal Petrie Cheops Rectangle Petrie¦CR.

Result: Both pyramid agents now have the same base and casing properties as the (for our quantitative test the remaining) Petrie measured Cheops Pyramid Petrie¦CP;

— All measures are now with respect to the Petrie height zero preference, the Petrie pavement platform.

— These arrangements establish the construction plan quantities. The end picture shows the two pyramid agents rJ¦CR with one and the same pyramid top and casing, where rJ has a 27.58’’ lower and 2×21,68’’ broader baseline situated below Petrie’s pavement: the CR agent’s zero level.

Bottom line:

— Guaranteed no one will be able to deduce or even imagine a clue to the construct unless rJ familiar. The edifice stays buried in a riddle, an enigma, until acquaintance is established.

— The rJCIRCLE¦GS-body quantities are (constructively) flat Petrie pavement pushed into the inside of the actual Petrie¦CR-pyramid. The result becomes an indexing CONSTRUCT for the 1883 actual Petrie measured Cheops Pyramid Petrie¦CP — proved by the corresponding quantities: the rJ agent defines Petrie’s measures.

CONTINUED DESCRIPTION: Introduction ¦ NatCH

The illustration below collects the basic main geometrical visual image concepts: What we need to advance, further.

THE GOLDEN SECTION BODY — ARITHMETICS — ArcTan½LINE — The GS-body — NatCH — The Golden Section Relation R = b/d = [√5 –1]/2 = 0.618033988:

GOLDEN SECTION EDIFICE — how the unique bd=h² pyramid triangle appears:

Leftmost [R¹↓, R² → , R³↑, etc.]:The Golden Section’s sectionally smaller squares with its quarter inscribed circles are built up as in an exponential series of the form

R^n with R=[√5 –1]/2. n denotes whole numbers only, beginning from n=0 giving a unit 1 = b = Cheops Rectangle triangle/pyramid’s half base.

Rightmost: Its [partial, almost exact] resemblance with the Nautilus Pompilius ”Pearl Boat Shell” (sw. Pärlbåtssnäckan). It is here denoted with a corresponding P for each consecutive [See deduction in GSbody]

Pn = b·R^[n—1] / √5. Each Pn is the actual normal [right angle] distance from the PearlShellEyeCentre to the GS-body envelope.

— All these definite geometrical quantities — exact measures — are our tools for analyzing and investigating any coupling between the GS-body and the 1883 Flinders Petrie thoroughly measured Cheops Rectangle. [Some authors name it Khufu Pyramid — after Modern Academic ideas in concern of an academic consensus of suitable origin].

— GENERAL with b=1:

bn = R^[n—1]: The Pyramid half base b1= R^0 = b. Next smaller GS-divided square is R^1 for b2, then R^2 for b3, etc.

— NOTE THE [50 M] DEEP WELL-TUNNEL NOT DRAWN OUT HERE with the so called Grotto in the middle [The Cheops Rectangle Circle origo — Latin: origin, not found in the English dictionary — from where the geometrical construct is made]. Petrie [Quote] gave no measures because of its uninviting feature. And nobody else seems to have: no specified measured quantities are known here. Different sources give different ideas of the actual path. See Help ILLUSTRATIONS.

— Quest: Is there any report from Egypt 2 500 B.C. that they knew about the Golden Section body ([5^½ –1]/2)^n structure?

A specific search @Internet 1Jan2020 on »golden section in ancient egypt» gives at least one PDF-based clarifying source titled

WERE THE FIBONACCI SERIES AND THE GOLDEN SECTION KNOWN IN ANCIENT EGYPT?, by Corrina Rossi and Christopher A. Tout, 2002:

” The conclusion is that concepts such as ϕ and the convergence to ϕ have little in common with the surviving ancient Egyptian mathematical documents and that they are quite far from the ancient Egyptian mentality.”; The PDF-source text sometimes misses an ”i”, here marked below:

” As for the first point, it might be suggested that the Egyptians had a geometrical concept of φ, just as the Greeks had a geometrical concept of π, and that they tried to approximate it using an infinite sequence of fractions. However, the first evidence of a geometrical concept of the Golden Section is to be found in Euclid’s Elements, dating to the third century BC (Fowler 1982), about 15 centuries after our Middle Kingdom scribes compiled their documents. No ancient Egyptian mathematical source contains any element which may be interpreted as pointing to an earlier knowledge of φ.”, p113mb.

There you go.

FONT NOTES: ϕ ϕ: definitely so drawn in the source text — but definitely so φ φ written when imported and converted by a Unicode Note Pad:

— The text source gives no mentioning. Dictionary Greek Alphabet (Swedish Lexicon) shows Φφ for our letters F f (sw.”fi”, eng. ”phi”): Microsoft WORD (Ctrl+Q, Font SYMBOL) shows , the latter sign apparently the same as in the quoted source text, not mentioning what the spell is supposed to be (it forces us to do what we don’t want to do: speculate on the content: ”we suppose they mean a small F”).

MathNote: Conv. ”Fibonacci series” include a more general outlook than only our ([√5 –1]/2)^n structure in this subject — but ”modern sources” seem not overly interested in presenting the strict geometrical Golden Section paragon as we do here (in connection to the Cheops Pyramid).

— What’s your point?

— IF the Egyptians didn’t know our ([√5 –1]/2)^n structure in this subject, who built the fit?

Check the correspondences.

Mission:

— What is our mission?

— To TEST and look for CLUES — as IF the Constructors had taken this stand:

— As clear, simple and straight as possible (5·8 + 18 = 58, etc.):

— Use NatCH the GS-body to RETRIEVE — recall — the way WE made the inner design: Try to find MATHEMATICALLY EASY — spelled: easy — PROVABLE reference points with which to control, test an check exact corresponding Petrie measures in a general quantity test.

CalCARDmethod:

We use two separate CalCards (TableA and TableB) organized as the one in The Result Table;

COMPARING VALUES:

We use TableA (rJCR¦b16-results) to fetch corresponding values from TableB (PetrieCR¦b58-results).

— With this arrangement we can easily and directly receive readouts (type: [G5+TableB.G5]/2) by a two party based average result — or other: We can easily test any [other] b-value agent as well.

— What The F-Word is a ”calCard”? It is just a more associative This Author’s term for [conv. spreadsheet, SS] a Computer aided Calculating Program:

— A ”specifically tagged calculating card” with specific reference capabilities — in the form of individual programmable cells collected in [rectangular] separate blocks;

— A smaller or bigger section of a programmable active spreadsheet. Type @Internet free OpenOffice

— My idea of the term came from MsWORKS 4.0 [Windows 3.1] where a LINKED part of a SS could be imported to a word processing program: Along with text, it appeared as a separate iconic CARD. By clicking the Card, it became active and editable/usable [classic Object Linking and Embedding]. It was in the beginning when [high speed turbo assembler] computer programming still seemed open AND FREE to Windows customers.

FIRST MOST SIMPLE AND DIRECT: 31Dec2019 ¦ FirstSimple: GS-body ¦ R-constant

PHASE 1 ¡ PHASE 2

FIRST SIMPLE OBSERVATION

A FIRST quantitative GALLERY TEST — from the rJCIRCLE fit.

Apart from the first obvious results in (Sw.ed.) CHEOPS REKTANGEL TabTest (Nov2017):

A First APPROVED MEAN AVERAGE FROM THE TWO PYRAMID AGENTS

Ref.: BPOINTMain:

In determining the B-point as 1 of The 7 fundamental Golden Section ArcTan½ Line points,

there are two GS-type fits: LOWER and UPPER visualizing a direct fit in the ascending passage’s breadth.

— The yB-difference of these is yATH with a yBlo = yB — yATH.

— Calculating the ArcTan½ slope where it intersects the Pyramids mid vertical in Point PG from yBlo, and using our Two Pyramid Agents respectively, we find their averaged mean on the vertical Pyramid centre to be

1657.78’’.

MEAN AVERAGED RESULT : FIRST »SIMPLE» OBSERVATION

Petrie’s value:

1658.20’’ ± 0.6, lowest 1657.60’’.

— Approved. Below is related even a more precise-near (1658.17) Petrie nominal value (1658.20).

— See also the ROSSI2002 reference:

— The ancient Egyptians hardly knew the math — as we understand it.

PETRIEpG: yPG ¦ FIRST ¦ pGconBuarm ¦ yConBUARM — calc.1658

THE GREAT STEP — Cheops Pyramid Gallery ramp top,

— See also THE LOST ANGLE.

Petrie does not give the direct ypGallery value 1658.20’’ ± 0.6. Its figure appears only through Petrie’s two specified components at The Great Step, up at the south end of the so called Grand Gallery part.

PetrieCH7.46:

”.. the height of the step face is 34.92 or 35 on E. ..”

”.. the step surface at the E. side of the S. doorway is 1693.2 ± .6 over the pavement.”;

— We calculate the difference as

1693.2 — 35 = 1658.2 (± 0.6)

(Some early @Internet picture photos show a severe injured site).

rJCIRCLEcalc.:

yPG: Actual yPG math ¦ PETRIEyPG

It is clear that the rJCIRCLE Cheops Pyramid construction plan has used a TRANSPOSITION EQUIVALENT

THE GALLERY-B-ENTRANCE-COURSE 19 CONNECTION

— same recurring constants at 3 different sites — between the B point (at ascending-descending) and the PG point (at Gallery ramp top) and the 19th course level and its thickness (TCA) of the form

GALLERY RAMP END GREAT STEP 3D drawing — Here FAIRLY RECONSTRUCTED FROM GIVEN MEASURES

———————————————————————————————————————————————————————————————————————————————————————————————

yATH ¦ BUARM ¦ yBlimit ¦ yPonB ¦ Fangle ¦ yBarm ¦ MiUNIT=100R ¦ bOFFSET ¦ 18

AT PG: yPG + 50R + yBlimit = 1693.1782168993’’ rounded 1693.20’’. Same Petrie identity.

AT PG: 50R + yBlimit = 35.0129561608’’ = 30.9016994375 + 4.1112567233. Same.

AT PG: yPG = [(rJCR¦b16=4555.88’’) — xB]/2 + yB — yBarm = 1658.1652607385 → 1658.17’’ → 1658.2’’. Same.

AT 19th:

Same. 3 different regions with the same used exact constants — defining Petrie’s measured values.

All the values mentioned by Petrie at the Gallery ramp top are rJCIRCLE-calculated-identified constants from the rJCIRCLE complex calculated B point.

BpointMAIN ¦ pGconBUARM

The same rJCIRCLE complex B point calculated quantities are used to define the thickness of the Petrie measured 19th course at the level of the casing entrance, and the (TCA) trigonometric/optical projection (Petrie19thProof) between these connecting the 19th course with the sloping angle of the descending passage.

— We underline here:

— This whole expedition is completely based on the 1883 Flinders Petrie working group measuring results. Through them only we (MISSION) SEEK corresponding clues, hints and leads to verify A The Most SIMPLE GS-body geometrical — exact — mathematical Origin, if at all. (No fancy creativity = zero speculation = zero doubt).

See also

Fangle ¦ Hangle ¦ Pangle

ConPent:

HOW PETRIE RECKONED THE Pyramid ENTRANCE GEOMETRY:

Petrie’s description follows in partial quotes.

All the following numbers are given from the Petrie quote in PetrieCH6¦31-32.

— Here we just relate the reckoning details — the figure below.

PETRIE MEASURES THE CHEOPS PYRAMID ENTRANCE — see following citations:

Related Trigonometric Specification: PREFIXxSIN is used in Universe History, unless otherwise mentioned:

— What means ”Prefix X sin” on my conventional scientific sin cos tan calculator? Just shift/think the labels SIN COS for COS SIN. Same buttons. Nothing else.

— Why the SINE prefix? Most animals are broad sighted —————— : The Horizon (x-axis) is the most viewed fundamental. Not the (co-) vertical.

c: CALCULATING h FROM e OR e FROM h ON GIVEN ANGLES AB — Deduction: Familiar with trigonometry (we always use the simple, straight and direct easy to remember PREFIXxSIN in Universe History) we have h/d=cosA giving d=h/cosA. Adding the two angles AB together gives

e/d=cos(A+B) with e = d · cos(A+B). The answer: e = h · cos(A+B)/cosA ¦ h = e · cosA / cos[A+B].

b: EXPLAINING THE TWO DIFFERENT TRIGONOMETRIC PREFIXES.

a: The Cheops Pyramid Complex rJCIRCLE Main Construct — origin of the nValue.

d: Actual Site: The Cheops Pyramid Entrance Complex, as described in PetrieCH6.32. TP1 ¦ TVTuS ¦ SumParts ¦ Petrie19thProof.

Petrie’s data along with PetrieCH7.35 ””:

” Having, then, fixed the original position of the doorway of the Pyramid, we may state that it was at

668.2 ± .1 above the pavement of the Pyramid;”,

PetrieCH7.35.;

” mean doorway height ¦ by measuring courses ¦ 37.94 ± .17”

”The data for calculating the result are

(1) levels of the 19th course by entrance 668.30 and 705.97;

(2) floor of passage at station mark, level 611.2

(3) which is inside the edge of the base of the casing horizontally, 638.4;

(4) entrance passage angle at mouth 26° 29' ± 1';

(5) entrance passage height 47.26.

” PetrieCH6.32.

— Petrie gives no actual written formula. But we can check and cross-check the values by using the above deduced connections:

PetrieConPent: PetrieCH6.32 Row32 Quote ¦

Petrie describes the 19th course thickness with a specified tolerance at most with

h = 37.94’’ ± 0.17 — with (Hih38.11, Low37.77) an end result for the floor normal e-factor above as

e = 47.26’’ (~47.3); PetrieCH6.32 Row56 ”(5) entrance passage height 47.26” gives the angles

A = 51° 53’ 20’’ ± 1’ ............ = 51.88888...° = 51 + 1/1.125 °: the PetrieCH6.32 Casing surface ”the face of the casing”;

B = 26° 29’ ± 1’ .................. =26.48333.... ° = 26 + 48/100 + 1/300 ° ; In PREFIXxSIN:

How Petrie took the reckoning grasp:

e = 37.94’’ · cos[51+1/1.125 + 26 +48/100 = 78.36888.. ]/cos[51+1/1.125] = 47.229552845’’.

— Taking these angles for given, the e-answer must use a lowest h = 37.964’’ to get a least rounded Petrie mentioned

e = 47.26’’ (47.25999..).

— However as the h-value can be as high as 37.94+0.17= 38.11, a type value of

h = 37.97 does the job for an e = 47.26 (Petrie gives no exact input parameters; as we see, there are ”many to chose on”).

— NOTE: Petrie explicitly names the e-part ”entrance passage height 47.26”, NOT a Vertical Height — which, through the simplified ArcTan½ angle should read

e · √1.25 = 52.84’’ — or 52.80068666’’ with PREFIXxSIN e(Vert) = e/sin(B=26° 29’).

But see these comparing results:

Petrie’s values with Petrie given tolerances matches the ideal corresponding

Golden Section paragon body Cheops Rectangle calculated quantities:

With all the differences contained inside the Petrie given tolerances

(hPetrieCP = 37.94’’ ± 0.17)

(ePetrieCP ; 47.26’’ ¦ 47.30’’ ; PetrieCH7.32, no specified tolerance:

”(5) entrance passage height 47.26”.)

it makes no change in the overall resulting picture if we select the Petrie given data or take the ideal received quantities from the rJCIRCLE complex:

with A = Petrie’s measured 51° 53’ 20’’

From e = 42.26’’:

B = ArcTan½ 26° 31 23’’ 26° 29’

h = 37.9529038928 37.9585978760 37.9640039644

PetrieLowestApproved h: 37.77’’

PetrieNominal 37.94’’

PetrieHighestApproved h: 38.11’’

— All apply.:

with A = Golden Section Cheops Rectangle ideal in PREFIXxSIN ArcSinR = 51° 49’ 38.25 25 43’’

From e = 42.26’’:

B = ArcTan½ 26° 31 23’’ 26° 29’

h = 37.9292286343 37.9349502165 37.9403824145

PetrieLowestApproved h: 37.77’’

PetrieNominal 37.94’’

PetrieHighestApproved h: 38.11’’:

37.95 row 2 RightLeft PETRIE

37.96 row 3 RightLeft PETRIE

37.96 row 4 RightLeft PETRIE

37.93 row 2 RightRight rJ ¦ NatCH

37.93 row 3 RightRight rJ NatCH

37.94 row 4 RightRight rJ NatCH

In fact, as we see, the latter part adopts more close to the Petrie referred nominal values (h=37.94).

— What does that result mean or prove?

— IllustrationPARTd emphasizes something like:

— GIVEN THE 19th COURSE FLOOR LEVEL (y19th = 668.2’’ ± 0.1) with its HEIGHT or thickness (Petrie’s averaged mean 37.94 ± 0.17) PRACTICALLY LITTLE OR NOTHING changes with a SMALL difference between an ideal casing angle A = ArcTan √1/R or the Petrie given slightly larger A = 51° 53’ 20’’.

In other words:

— The Petrie given data will NOT have any priority over the rJCIRCLE calculated quantities:

y19th h

PetrieCP 668.2 ± 0.1 37.94 ± 0.17

PetrieCR 668.1482038706 37.9403824145 with rJCR

See Enter The Petrie19thProof

ConPentRes:

RESULT:

In other words, as no notified detail interferes with the conclusion:

— The rJCIRCLE complex CAN

most exclusively and gallantly quantitatively as this part as shown

be comprehended as a DEFINITION of the (very gallantly performed) Petrie measuring conditions.

PetrieQuote19th:

Petrie comes to the point ”entrance passage height 47.26” In Quote PetrieCH6.31 Row43.

QUOTING PETRIE

The Petrie ConPent illustrated math.

Petrie writes In Quote PetrieCH6.31 Row1 on TCA;

Petrie takes arguments from other pyramids In Quote PetrieCH6.32 Row11.

— See in explicit: Proving the 19th Course Arithmetics:

————————————————————

ENTER ¦ MainConstruct ¦ SummingParts ¦ ThePush

————————————————————

— The two pyramid agents define the nValue subterranean 2n STRIPE in which midpoint the Petrie vertical G-point ’’1181 ± 1?’’ becomes identified:

— Summing the n-value with the entrance ideal rJ-calculated A point vertical height value 665.34’’, practically in a direct hit, identifies Petrie’s defined 19th floor height above the pavement (668.20’’ ± 0.10). The rJ values present the close 668.15’’ or 668.16’’ depending on choice of preference (original n, or an adopted convenient pi-value for the hypotenuse side to the n value triangle, whichever is legal). By this order, the bottom (G) an top (A) pyramid inner design construct parameters unite and become certified.

Note that Petrie is giving a more precise height value (668.20 ± 0.1) in PetrieCH7.35b¦36e¦64tab which allows the Petrie In Quote PetrieCH6.32 Row52 stated ”668.3” for the height of the entrance point — same as the 19th course floor level.

— We use the Petrie tabled value 668.2’’ ± 0.1 to refer Petrie’s presented value on the 19th course floor as a nominal measure of The Petrie Measured Entrance Point.

The Gallery point pG: The B-point ¦ PHASE 1 — ORIENTATION

GalCalcOW — 2: GCOW1

GALLERY CALCULATIONS OVERVIEW part 2

THE GALLERY-B-ENTRANCE-19th

COURSE CONNECTION

The illustration clarifies how the Golden Section paragon geometry through the rJCR¦b16 agent differs from the actual Petrie measured Cheops Pyramid physics. All differences between these are now calculable and so provable, as it has shown.

— Withe The Contracted bOFFSET push [building constants define the 19th course thickness by trigonometric/optic projection], these two will share the same descending roof. See ThePush1. See also the main Cheops Pyramid rJCIRCLE proof on THE CONTRACTED CONSTRUCT.

Add1.84: yBPcon — TVTus

yAdd1.84 = xBPcon/2 = yBPcon

xBPetrieContracted = xB¦rJ — (xB¦rJ + 18 — bOFFSET) = bOFFSET — 18 = x;

yBPetrieContracted = x · Tan ArcTan½ = x /2 = 1.84 = yBPcon

With a final projecting bOFFSET PUSH (TP1) between the two pyramid agents

all acquired calculated constants contribute to a single and final proving end result:

— The explaining connection between the (Crucial—Row43) Petrie original explained 19th course and its trigonometrically/optically projected entrance (TCA):

cSideSUMMINGillustration: cSIDE = 52.889142448’’ ¦ yBPcon

————————————————————————

yATH ¦ yBlimit ¦ BUARM ¦ yBPcon ¦

For clarity. The cSIDE then determines the thickness of the 19th course in a final optic/trigonometric projection. See Proving the 19th, also in copy below.

— As seen: It is fundamentally impossible to deduce the construction PLAN — proving the quantities within the Petrie given tolerances — WITHOUT familiarity with the rJCIRCLE complex , the two pyramid agents. They alone are responsible for the entire quantitative edifice’s general mathematics.

As we know, see also ROSSI2002: The level of mathematics in ancient Egypt had no such familiarity. So capitulating in front of an overwhelmingly scientific fact, unless there is still more wonders to discover: The building was set up a long time before, from an engineering source we deeply and painfully are completely ignorant of, except for The Great Artifact.

— Our painful ignorance deepens considerably in a broader sense with Petrie’s illuminating description of this Casing-Tunneling projecting principle (TCA) as representative for OTHER PYRAMIDS TOO, some located far from the most Northern Egypt Cairo-Gizeh location (PetrieCH6.2 In Quote Row12): same principal/principle construct.

Possibly but completely unknown here: all of them. It is impossible to avoid An Associate to South American pyramids too, with our ignorant level as our guide. We need Explanations obviously outside the horizon of modern academic ideation.

The D-form is the same type as in yConBoffset.

See also the summing parts in ThePUSH 1.

Summing the different parts together defines the Petrie measured [37.94’’ ± 0.17] Cheops Pyramid 19th masonry course height: The onset quantity of all the Petrie measured details of the Pyramid’s inner design. See SumParts, Petrie19th proof, and ThePush1. PREFIXxSIN in TrigRef.

A: Cangle = ArcTan1/R^½. B: Pangle = 26° 31’ 18’’.

— The yATH and the BUARM — so — finalizes the calculation expedition in also defining the Petrie measured 19th floor stone masonry course thickness (37.94’’ ± 0.17) at the Pyramid’s North entrance at ENTER A.

LINE pi has no connection to the number pi.

2R = 5^½ — 1 = 0.618033988..

— See (TP1) the Petrie19th proof through the summing up (SumParts) of all the named parts

c = yATH + yBlimit + BUARM + (bOFFSET — 18)/2

c = 43.37 + 4.11 +3.57 + 1.84 = 52.89’’; paralleling this value gives the shortest tunnel normal

(52.89)/(1.25)^½ = 47.31’’ (= 47.3054871141)

A final trigonometric transformation from entrance slope to horizontal masonry course through the casing slope — Petrie’s specific 51° 53’ or our ideal Cheops Rectangle 51° 49’:

— both ways give practically the same end result. They define the same Petrie 19th course thickness:

— As calculated (TheTrigonometricTransformation) with Petrie’s values in PREFIXxSIN

37.9529038928’’ = cos(A=51° 53’’ 20’’) · 47.26/cos(A + [B = ArcTan½ = 26° 33’ 54.18 42 37’’])

37.9640590055’’ = cos(A=51° 53’’ 20’’) · 47.26/cos(A + [B = 26° 31’ 23’’])

37.9640039644’’ = cos(A=51° 53’’ 20’’) · 47.26/cos(A + [B = 26° 29’])

As calculated by the above rJ-summing and the trigonometric transformation,

GENERAL GS-body: ¦ ArcTan 1/√R = Cangle = A = 51° 49’ 38.25’’ = ArcCot√R ¦ sinA = R ¦ cosA = √R ¦

37.9657350065’’ = √R · (c=47.3054871141) / cos(A+ ArcTan½)

— Approved:

— There is no significant difference between any of these in

the PetrieCH6.31 Row32 given specification,

37.94’’ ± 0.17. The resp. differences are:

0.0129038928 ¦ B = ArcTan½

0.0185978754 ¦ B = 26° 31’ 23’’

0.0240039644 ¦ B = 26° 29’

0.0257350065 ¦ rJ

All these lie well within the Petrie given ± 0.17’’.

PHASE2: BpointMAIN ¦ The B-point ¦ PHASE 2 — ORIENTATION ¦

PHASE 2 first ................. First part: FINDING THE pGpoint

PHASE 2 second ............ Second part: FINDING THE Petrie Measuring B-point

The B-POINT

Designing the Cheops Pyramid — false statements are not allowed here ¦ So: If I’m wrong, I have to be cremated. Have mercy on our souls.

SEE SHORT INTRODUCTION IN NatCH

PHASE 2

Quantitative Determination of The Basic Properties

The term CHEOPS RECTANGLE was adopted by this author after a late 20th century detective search in libraries of the most early known mentioning of the unique and very geometrical-developing useful connection bd=h². It was rhetorically used by Galileo Galilei, Apollonios and Pythagoras, further backwards mentioned as an Egyptian ancient form connected to the Cheops Pyramid. We respect that tradition here, and adopt the term to it.

Orientation — UpperGS ¦ LowerGS ¦ yATH ¦ yConOFFSET ¦ BUARM ¦ yConBUARM ¦ pGconBuarm

Orientation: Phase2

BPOINTmain: Bpoint

GENERAL:

The B-point connects the rest of the Petrie measured interior Cheops Pyramid design with the basic Construction Line (The 7 Points). Here we directly find a Petrie (1658.2±0.6) matching/defining correspondence with the Gallery point (PG) through the two pyramid agents and their combined (related, simple) quantity results. The illustration below shows the rJCIRCLEcomplex B point calculated details and the following text explains them, unless already familiar.

yBarm ¦ yATH ¦ BUARM ¦ PetrieBpoint

DESCRIPTION:

Having certified the A-point (PHASE1) by the same ENTER entrance on the ArcTan½-line lying and so genuinely asserting points KLM,

the next important GS-body paragon xy-position to determine is the B-point:

— The B-point is the GS-CONSTRUCTIVE layout’s most crucial intersection point (best to mention in eliminating any possible misunderstanding): uniting a down and up measuring reference.

— The B-intersection is ideally Golden Section calculated between the already given descending passage ArcTan½ and its ascending ArcTan½ spouse, the Petrie named Ascending Passage upwards in to the Gallery part.

There are in explicit two differently positioned GS-candidates showing a visual fit with the ascending passage’s ArcTan½-tunnel:

UPPER:

— One GS-candidate touches the lower part of the ascending passage, the floor part;

LOWER:

— One GS-candidate touches the higher part of the ascending passage, the roof part;

— These two are calculated from the GS-body as follows:

UPPER-GS¦Ascending tunnel roof:

PaLINE → :

x(Pa) = bR^5 = b6

y(Pa) = b(R — 1/√5) = b2 — P

PbLINE → we borrow these xy from the already given LINExy-values

x(Pb) = Lx —b(R/√5 + R^3) = —(PiLINEx + b4)

y(Pb) = Ly b(1/√5 — 1/2) = P — b/2

— The LIC line intersecting connection gives the GS top upper B-point rJCIRCLE¦b16 root ascending tunnel reference xy-values as

Bx —1499.7016293661’’

By 177.0157652488’’

LOWER-GS¦Ascending tunnel floor:

— We only use the xy-position on the GS-body touching -ArcTan½ ideal geometrically constructive tunnel ascending floor: With this xy(Pa) point given on the GS-paragon structure, we only have to take its y-axis intercept (see LIC) and subtract its value from the already above given xyB-point value (-572.83504943) in order to receive the offset difference

(The ideal rJCIRCLE¦CR vertical ascending tunnel height from point B):

— In this expedition we (try to, with no compromising) use Pa for the upper ascending negative ArcTan½ and Pb for the lower descending positive ArcTan½ (after Petrie’s namings).

— For the trigonometric 0.8 and 0.2 parts, see explanation in b5REF unless already familiar.

x(Pa) = —b(R/√5 + R^5 + √0.2 · R^4) = —(PiLINEx + b6 + √0.2 · b5)

y(Pa) = b(1/√5 — R^3 — √0.8 · R^4) = P — b4 — √0.8 · b5

yATH: Ascending Tunnel Height, ATH

The y-intercept for this positioned -ArcTan½-line is -616.2046894218’’;

— Taking the difference gives the rJCR¦b16 vertical construction height

yATH = ROOF¦vert. — FLOOR¦vert. = 43.3696399875’’:

The Construct LayoutAscendingTunnelHEIGHT from point B — AscTunHEIGHT,

here denoted yATH:

yATH = 43.37’’ — rJCR¦b16-determined = 43.3696399875’’

We mark this value as The Basic Nominal Constructive value for the ascending tunnel height.

BUT:

We would be, really, The F-Word up if this would be the final GS-constructively suggested result.

— What’s the hang?

— We need an additional BUARM — for securing the Gallery Top Slope PG-point.

— A B-point Upper Ascending ROOF (BUARM) Averaged MEAN.

We study that.

First: Adding the yConOFFSET — for pending comparing purposes

The yConOFFSET is a fix property that can (possibly) be used in our further testing quantities. We study how.

In TABLE OF RESULTS

we already have the rJCR¦b16 xyG-coordinates:

— Taking the corresponding PetrieCR¦b58 coordinates establishes the actual construction plan — here to be investigated in deep. Selecting a ”1” in the calculus card we receive the comparing corresponding PetrieCR¦b58 values as follows:

yConOFFSET: See details in ConAG

These two are connected by a fix, solid exact internal xy-horizontal-vertical differing separating offset value. Their y-intercepting non alterable constructive difference is

G(rJCR¦b16)Ny — G(PetrieCR¦b58)Ny =

yConOFFSET = 4.4106512044’’

BUARM: With a PetrieCR¦b58 4534.20’’ ideal Cheops Rectangle corresponding ascending quantity design layout, we have the B-point references for the upper ROOF part from the only two available construction coordinators rJCR¦b16 and PetrieCR¦b58 as

BUARM: BUARM ILLUSTRATED in BPOINTmain

TWO SLIGHTLY DIFFERENT B-COORDINATES ARE GIVEN BY THE TWO DIFFERENT AGENTS

(|x1| — |x2|) = 7.14’’ → ;

[xATH(rJCR¦b16) — xATH(PetrieCR¦b58)]/2 = (1499.70 — 1492.57)/2 = 3.57’’, meaning:

— On the ArcTan½ right angle triangle: (x1 — x2) ½ = (y1 — y2):

— 3.57’’ is an exact (2 decimal rounded) geometrical BUARM,

B-point UpperAscendingROOF (BUARM) Averaged MEAN Vertical Difference between the two pyramid construction agencies rJCR¦b16 and the ideal Cheops Rectangle PetrieCR¦b58: »best provision».

BUARM = 3.57’’ = 3.5682917806’’

Options — see The AG-Condition:

— In general (result from the AG-condition): ONLY the rJCR¦b16 pyramid agency will have priority on a fixed geometrical parallel relationship with the ideal PetrieCR¦b58 spouse. Meaning:

— The ideal PetrieCR¦b58 agent CAN make ”averaging means” together with the main rJCR-agent.

Meaning:

— EXTENDING OUR simple and direct POSSIBILITIES (for us to find, and the constructors to form) in finding true (and exact) quantitative matches with the real physical PetrieCP Cheops Pyramid measurements from 1883.

yConBUARM: yCon ¦ BUARM ¦ tyATH ¦ aVA ¦ Con ¦

yBarm ¦ yBarmILLUSTRATED

The GS-body then SUGGESTS that the B-point with agent PetrieCR works like this:

— AS the agent PetrieCR has no other possible parallel relationship with agent rJCR than in the G.point determination, see conAG, we use agent PetrieCR to give us an ADDITIONAL AVERAGED MEAN from

• (y1 — y2)/(x1 — x2) = ½ for the PetrieCR¦b58 ROOF -ArcTan½-line, so that

• (y1 — y2) = (x1 — x2) ½;

— (x1 — x2) = 2 BUARM =

= 7.14’’ = ;

Given an x-value on a right angled ArcTan½-triangle, the y-value appears as a simple x/2:

• [(x1 — x2)/2=3.57’’ = BUARM

+ (yConOFFSET=4.41)] / 2 = averaged VERTICAL ADDITION mean value:

aVA = 3.99’’;

The GS-SUGGESTED Pyramid nominal CONSTRUCTION (Con) VALUE,

yATH-value (43.37’’), will then have

a longer (OPTIONAL) version added with aVA as a total (t)

tyATHyConAssociate = 43.37 + 3.99 = 47.36’’ = yATH + aVA.

Total vertical (y) distance RoofFloor Ascending TunnelHeight:

tyATHyConAssociate ....... = 47.36’’.

— In figures, this VERTICAL value is nearly the same as (HowPetrieReck) the PetrieCH6.31 measured/calculated PARALLEL descending entrance value (e=) 47,36’’:

— This tyATH result 47.36 value has no further meaning or use here, as we know of.

With only the addition of BUARM — we leave yConOFFSET and aVA — we have

tyATHyBUARMAssociate ... = 46.94’’ = 43.37 + 3.57 = yATH + BUARM = yBarm:

Which we name

yBarm = 46.94’’ = yATH + BUARM = 46.9379317681’’;

yBARMillustration: BUARM ¦ yPonB — Addition to SIO and yConB — ¦ yBlow ¦

THE CONTRACTED CONSTRUCT view.

SEE also part ILLUSTRATION IN TheConstruct and partly in GalCalcOW1. Here with some additional details (yBlimit ¦ yConBoffset ¦ yConB) for the proceeding:

As we know: the yConOFFSET quantity no longer

has any specific role to play from here apart from its fixed ConAG property as a pyramid agency.

+ 43.37 ......... = yATH

+ 4.11 ........... = yBlimit = yConB + yConBoffset = yConHBALimit = yConB + SIO

+ 3.57 ........... = BUARM

+ 1.84 ........... = [ bOFFSET — 18 ] / 2 = yBPcon — trivial Result from bOFFSET contraction

———————

= 52.89 = cSIDE

/ √1.25

= 47.31

— The difference in leaving yConOFFSET and aVA is 0.42’’

— The yB associated yBarm y-ccordinate then becomes

(yB=177.02) — (yBarm=46.94) = 130.08’’ = yBLow;

yBLow = 130.08’’ = yB — (yATH + BUARM = BUARMyATH = yBarm)

With these parametric contributors we can make a full test on the Gallery sloping floor top, the vertical midpoint of the Pyramid, for comparison with the Petrie measured values:

pG(Con) and pG(BUARM): yATH ¦ BUARM ¦ yConBUARM ¦ yConOFFSET ¦ yPG ¦ yPGcalc

PetrieCH7.46 Col1 Row18 gives only an indirect pG-point value:

He refers the top step surface by [PetrieRow42] 1693.2’’ ± 0.6 with a below step face socle height value as ”34.9 or 35”, or [PetrieRow34] 34.88 ”above actual floor end” depending on detailed more or less injured location. Summing these figures, and caring on Petries tolerance specification makes an allowed Petrie1658

—35+1693.2=1658.2 with the vertically Petrie mentioned 1693.2 adopted tolerance: ± 0.60.

— Using only the BUARM

y-offset 3.57’’ + yATH(43.37) = 46.94’’ = yBarm we have [ArcTan½ triangle x/2=y]

y(PG) = 1658.17’’ — only 0.03’’ from Petrie’s nominal:

yPG¦rJCRb16 =

[(rJCR¦b16=4555.88) — 1499.7¦xB]/2

+ 177.02¦yB — 46.94¦yBarm

= 1658.17¦1658.1652607385

— Both end values lie well within Petrie’s given tolerance ±0.6. See also The TRANSPOSITION EQUIVALENT.

In expliocit: Petrie’s socle height (35’’) is rJCIRCLE identified with an ideal single value

50R + yBlimit = 35.0129561608’’ = 30.9016994375 + 4.1112567233. And so Petrie’s level 1693.2 is rJCIRCLE identified as

yPG + 50R + yBlimit = 1693.1782168993’’ rounded 1693.20’’. Same identity.

— Approved.

yPG rJ-calculated from B point: [(rJCR¦b16=4555.88) — xB]/2 + yB — yBarm = 1658.1652607385 → 1658.17’’ → 1658.2’’: ArcTan½-math: Petrie 1658.2 Quote:

1658.20 ± 0.6.

The rJCIRCLE complex calculated yPG level value

1658.17’’ = yPG = 1658.1652607385’’ → 1658.20’’.

ArcTan½-math: .............. (b1 + b1xB)/2 + b1yB — [yBarm = yATH + (BUARM=GSintersectionDiff)] = 1658.1652607385’’ ....... rJCR¦b16 = b1

APART FROM OTHER POSSIBLE CANDIDATES this result is — as known here — the closest we can get to the Petrie corresponding nominal yPG = 1658.2’: Difference 0.03’’ — in allowed ± 0.6’’. A direct hit.

There was also another (near close, approved) match along with the above two — see FIRST.

PHASE 1 — THE CONSTRUCTION LINE ¦ PHASE 2 — THE B POINT —— Phase2.1 — FINDING THE pGpoint ¦ Phase 2.2 — FINDING THE Petrie Measuring B-point

ConMes: CONSTRUCT AND MEASUREm overview

The Construct and The Measure

THE CONSTRUCT AND THE MEASURE — just a short overview

How

The 7 Points Determined Construction B-point appears

— Construct and Measure have different preferences: The Construct is impossible to deduce from the Measured building quantities the underlying rJCIRCLE complex is understood: the construct plan.

See also further below in Explaining the Construct.

TheConstruct@B — BASIC: THE yCON OFFSET VALUE BETWEEN THE TWO PYRAMID AGENTS IS PRESERVED.

yConOffset DETAILS IN ConAG.

————————————————

yConOFFSET

ab-values from GS-paragon UpperGSroof on comparing rJCR¦b16 and PetrieCR¦b58. cd-values from UpperGSroof AND LowerGSfloor. e-values from the ab-set.

See in explicit

The pG-value calculation via B,

The TRANSPOSITION B.PG.

TheMeasuredConstruct@B — Petrie point B:

See further below in Explaining the Construct and ThePush.

— The numbers 50.76 and 74.19 is mentioned (quote continues PetrieCH7.38):

” Further, the lower end of the plug-block is

74.19 from the intersection of the floors; and the upper end

50.76 from the intersection of the roofs. Having thus fixed the beginning of the Ascending passage, by the point where its floor produced onwards intersects the floor of the entrance passage, we can proceed up the Ascending passage from this as a starting point.”.

MISSING PETRIE INFORMATION?

NOTES ON PETRIE’s VALUES IN tunnel POINT B — missing data?

— No. But a clarification in needed here.

PetrieCH7.38:

”.. with

26° 21' as the descending angle at that spot (by Prof Smyth),

the Ascending passage roof starts vertically over

1110.90 on the sloping floor of the [p. 62] entrance,

reckoning from the casing face; and the floor cuts the entrance floor at

1110.64 from the same, both probably ± .1.”. No clue.

” The junction of the passages was not projected over the broken part uncertainly, as had been done before; but a plumb-line was hung from the W. side of the Ascending passage roof, in front of the plug-blocks; and measures vertical, perpendicular, and sloping, were taken to the plugs, the fragments of the ascending, and the top and bottom of the entrance passage. Thus the whole was knit together to a true vertical line, the place of which was fixed on the entrance floor. From the mean of these measures, and

26° 12½ ' as the ascending angle, with

26° 21' as the descending angle at that spot (by Prof Smyth), the Ascending passage roof starts vertically over

1110.90 on the sloping floor of the [p. 62] entrance, reckoning from the casing face; and the floor cuts the entrance floor at

1110.64 from the same, both probably ± .1.”. No clue.

In dissecting Petrie’s statements in parts an answer shows up in full:

The illustration clarifies the aim:

— There is a small difference (not visible in the 10 inch scale) between

the roof (AscendingDescending) intersecting point

vertically aligned with the Petrie xyB-point from PetrieCH7.64tab

xB¦1517.80±0.30

yB¦172.90±0.20

and the floor intersecting point (AscendingDescending):

— The latter is pushed 0.26’’ up-ways north the entrance.

HOWEVER: PetrieCH7.64tab gives for the xB-coordinate the measuring tolerance

± 0.30, which obviously overrides the

0.26’’ floor up north intersecting deviation (horizontal 0.23’’ through the angle 26° 21’).

— So: From our Cheops Rectangle investigation viewpoint, the Petrie noted UpNorth 0.23’’ horizontal difference will have no effect on this expedition — unless other arguments will show up.

Petrie F° Angle: — The actual physical [mean averaged] floor angle between subterranean [P] and Petrie’s B-point where descending meets ascending — compiled 27Feb2020

THE ACTUAL PHYSICAL descending FLOOR ANGLE(s)

The FANGLE

ArcTan(yG — nVALUE + yB — yBlimit)/(xG + 10R — xB — 18) = 26.5479489261° = 26° 32’ 52.61 61 34’’

THE COMPOSITE ANGULAR COMPLEX — The yPonB secret

AS IT HAS SHOWN:

How the descending tunnel HAD to be constructed physically in order for the Petrie working group to get a spot on (TCA, see full Petrie Quote) The Central Aspect: the 19th floor and its decisive projective connection to the descending passage — exactly by a TCA principle as described by Petrie.

a: The Construct’s Plan: If this would be the final cut, the actual Petrie measured values would be catastrophic.

— Why is that?

b: Spotting the Casing Rim (O) from the tunnel (P or H) would clearly miss the point if the tunnel floor would finalize on the line PO of the a-construct planning level: Petrie’s Cogitated Principle (See full Petrie Quote) with the 19th floor level;

— Its block course masonry thickness — at the level of the entrance — features a trigonometric/optical PROJECTION (The TCA principle):

THE CENTRAL ASPECT: The Whole Inner Design Pyramid Plan

Cheops Pyramid — SEE THIS CENTRAL PROJECTING PRINCIPLE MORE IN DETAIL FROM PETRIE’S DESCRIPTION IN PetrieTCA.

A UNION APPEARS between descending passage and actual course.

In other words:

— Some additional floor height (Fangle) of the a-construct planning level is needed to GUIDE a measuring optical instrument AT

the actual Petrie measured/observed Casing Spot:

— The yPonB quantity:

THE yPonB quantity secures a safe optical lower limit visual sight line window through the descending passage through which safely spotting the decisive Petrie PC point on the Pyramid casing rim. See full details from ENTER.

So?

— What MATHEMATICALLY SHINY INSTANCE COULD PROVIDE such an ”additional floor height” above the actual construction plan for the Cheops Pyramid building?

BY EXACT MATHEMATICAL GEOMETRICAL DEFINED QUANTITIES:

— The rJCIRCLE definition of the Petrie measuring B-point (The Petrie B point):

PROOF:

— Using intersection mathematics — same as optical sight line intersections — on the acquired different angles (Fangle, Pangle and Hangle) from the given defined Petrie measured values with Petrie’s given tolerances, defines a narrow Pyramid casing visual optical window between the MO points as compiled below.

SEE ALSO THE nVALUE FROM ENTER: yA + nVALUE = 19th FLOOR vertical level: 668.1482038706’’. PetrieCH7.35: ”668.2 ± 0.1”.

OVER AND OVER AGAIN, WE FIND THAT THE rJCIRCLE calculated quantities DO — well — define Petrie’s measured values as taken within the Petrie specified tolerances. See also IntroEX.

The Petrie spotted point pA — Petrie’s instrumentally claimed Pyramid original casing point on the 19th course floor level — has the Cheops Rectangle Pyramid Ideal Casing point O as an absolute lower visual sight line along the actually constructed descending floor, as the rJCIRCLE construct plan is explained through this result.

— The upper limiting sight line from Petrie B to the casing rim surface guarantees a narrow optical spotting window framing the decisive point pA. The metric casing difference between the lower floor spotting limit and the actual pA point extension is no more than 0.23’’ (roughly and ideally slightly less than [0.25’’]/√1.25=0.2236’’) — provided an ideal flat B.M even precision tunnel floor with no deviations.

So:

— The whole angular and coordinate/measuring point descending passage complex can (now, finally) be viewed in the following more precise detail:

STRONGLY EXAGGERATED ANGLES FOR CLARIFYING THE EXPLAINING CONSTRUCT PICTURE: General tunnel angles

SummingTCA:

SUMMING:

— All construction planning in detail. High Tech Math.

— But what if the old modern academic Egyptians who are said by these more modern inventors to have built the devise were psychic: they knew all these features directly from Within?

— Happy them. We are outclassed. Shredded. I am so sorry for having taking up your precious time.

Aftermath — at first, during some time ..

IN Attempting to compose an overall describing picture of the Petrie given angles and measured points of the descending tunnel between casing (A) and tunnel end (P), nothing made sense.

So it was until a specific Petrie F°angle (Fangle) was identified between the Petrie measured points: the subterranean (P) and, nearest mentioned above the pavement, point B:

— Petrie neither mentions any measured connection (from the subterranean site) to the in-between lying H-point — the point where the descending tunnel meets the pyramid’s baseline.

Petrie’s FloorAngle P.B — Fangle, the actual physical floor, as here understood — is never [directly] mentioned in any angular value in Petrie’s Chapter 7 descriptions.

— Reckoning the Petrie xy coordinate values between

4228;1181 and

1517.8;172.9

gives Fangle =

26° 32’ 41’’

— slightly different from the general Petrie 4140 inches long descending passage stated thoroughly averaged mean

”26° 31’ 23’’ ± 5’’ ?”.

ExCon: TheConstruct

EXPLAINING THE CONSTRUCT IN QUANTITATIVE DETAIL

The Construct — in detail

With given P angle (»Pangle») and H angle (»Hangle») the floor offset construction points can be calculated — exactly.

Pangle and Hangle define

THE DESCENDING PASSAGE FLOOR CONSTRUCT LAYOUT ANGLES:

— See how The Petrie Point explains why a descending FLOOR BREAK (@H) must exist

to connect the Construct Plan to the entrance point (A), thereby granting the main construction line to be buried inside the building, never exposed in the actual visual edifice construct.

The descending and breaking floor construction trimming reference values will then appear directly as follows:

yConB: ExCON

yPangleHend — yHangleBend.

THE DESCENDING FLOOR SLOPE will be constructively determined from the Petrie P point (P) through the P angle (lowest Petrie 26° 31’ 18’’).

Through the floor breach @H, the floor directs to the entrance point A though the slightly smaller H angle (Petrie 26° 29’ ± 1’).

Summing the continuity of this floor-construct gives a reference point yConB @B valued

yConB = yPangle@H-end + yHangle@B-end =

3.0124757861’’ = yConB

above the nominal rJCR¦b16 calculated yB-value yB = 177.0157652488’’.

— We will see how this point CAN rJCR¦b16-DETERMINE the actual Petrie B- measuring point which connects the Petrie measuring descending and ascending passages.

rJCR¦b16-DETERMINATION

THE ACTUAL PETRIE B- MEASURING POINT

rJCR¦b16-DETERMINATION of the actual Petrie B- measuring point

is realized as follows — it all connects to the Petrie 19th stone masonry course, 18th course roof value (Petrie 668.2’’ ± 0.1):

yConBoffset: n — D = 1.10’’ ¦ FOR PREFIXxSIN, SEE TRIGREF unless already familiar ¦ Finding d ¦ THE D-FORM IS THE SAME AS THE ONE USED IN ADD1.84 ¦ yConB

yConBOFFSET = SIO = 1.0982940329’’:

EXPLANATION — the yConB-offset finishes the entrance passage construction math:

— The Petrie stated descending slope angle P-point related ”26° 31’ 23’’ ± 5’’ ?” travels by distance d (Finding d: 2.13236805’’, see table Result Basics), ending on the ideal Cheops Rectangle Golden Section Casing Pyramid near point A;

COMPLEMENTARY EXPLAINING CONNECTIONS: yBlimit = yConB + SIO

The Petrie F°Angle — Line SubterraneanPetrieP.PetrieB as known: never described by Petrie himself in terms of a specific angular value — is described in a separate section. See Fangle. This illustrations clarifies how the constants yBlimit = yConB + SIO appear from the yConB angular connections between details below and above [H] the pyramid baseline reference [Petrie’s pavement], here at point region B.

— yPonB is apparently a constructive BONUS.

SecureInspectionOffset, SIO: D18 ¦ yConBoffset

— As the bottom passage G-region n-value (hypo side in the ArcTan½ triangle) through the adopted pi-value in calculating the P-angle is

π/(1.25)^½ = 2.8099258924’’,

also equal to the Petrie’s measured 19th course floor value 668.2’’ ± 0.1 by

(yA¦rJCR¦b16 = 665.34’’) + [π/(1.25)^½ = 2.81’’] = 668.15’’ ............... Well APPROVED,

»we» CAN use this additional »fillOut» d→A projected difference

n — (D=1.7116318595 — on Casing point A) = 1.0982940329’’ =

yConBoffset = SIO = n — »D18»

SIO = 1.0982940329’’ ................................ yConBoffset = SECURE INSPECTION OFFSET, SIO

as an »inspection guard» or

A GRANTED INSPECTION OFFSET — A »The» decisive Petrie observing LEAD:

— See detailed in Proving the 19th ¦ yBarmILLUSTRATION ¦ TP1DET .

yBarm ILLUSTRATION ¦ TP1Det ¦ Course thickness D — Proving the 19th

— See also The Petrie Quote in How Petrie Reckoned the Entrance Geometry, the central

— from the 19th course floor height (668.2’’ ± 0.1), Everything in the inner design of the pyramid, all the measures, depends on the onset of that measure.

yBlimit SIO

— Adding the SIO=yConBoffset value to the yConB-point gives a final

4.1112567233’’ = yConB + yConBoffset =

yConHBALimit = yConB + SIO = yBlimit

yBlimit = 4.1112567233’’ = yConB + SIO

............ SECURE CONSTRUCT ENTRANCE PASSAGE FLOOR LIMIT @B, yBlimit

on top of the yB = 177.0157652488’’ value.

Claifying yBlimit resolution:

So (again):

— What is the meaning of this yConHBALimit = yConB + yConBoffset?

— Obviously the simple Petrie introducing Main Measure:

The (Constructors) meaning is obviously to arrive at a measuring ENTER SPOT of the 19th course floor value — AT some Petrie staircase masonry remaining sloping angle:

— The PetrieCh7.35: 51° 53’’ 28.60’’: the Petrie Cheops Pyramid remaining staircase masonry sloping angle at the northern entrance site as seen/measured with respect to the whole tunnel.

— The yConB part 3.01’’ from the H-floor breach @B, plus the additional remaining SIO 1.10’’ yConBoffset, FILLS UP up the remaining space to the 19th course floor — on the Petrie (idea of the original) Casing, as he mentions it (”.. and the face of the casing ..”, see the entire Quote).

RelatedPetrieSPOT: yBlimit

In Short:

— (Vertical) OFFSETS (by given angles) above the construction plan must be given in order to secure a safe (and precise) measuring spot on the Pyramid casing as seen from the tunnel: the projective connection between descending passage and the 19th course floor and its masonry height (37.94’’) at the level of the entrance.

See in detail from Proving the 19th ¦ Enter ¦ Fangle ¦ PetrieCH6.31 whole Quote .

Or as Petrie states the general status of (some parts of) the edifice himself

(Quote from another web site):

”.. it is to be compared to the finest opticians' work on the scale of acres.”.

The Petrie B-point. Phase 2.2: — PetrieBpoint: RELATED PETRIE SPOT

The final Test: The Petrie B-point

PHASE II.2: FINDING THE Petrie Measuring B-point — no dramatic issue

See also PHASE II.1: The B-point FIRST PART

In PetrieCH7.39¦64tab Petrie gives the xy(B) values

xB 1517.8 ± .3

yB 172.9 ± .2 ............................ website source corrected from table error. Petrie gives correct value in CH7.39

We [PHASE 1—Table Results] calculate the corresponding rJCR¦b16 agent values from the previous results and arrive at

xB: 1499.70 + 18 ...................... = 1517.70 ............... approved ¦ Petrie: 1517.8 ± 0.3

1499.7016293661 + 18 ................. = 1517.7016293661

xB + 18

yB 177.02 — 4.11 ...................... = 172.91 ................. approved ¦ Petrie: 172.9 ± 0.2

177.0157652488 — 4.1112567233 ... = 172.9045085255

yB — yBlimit

— We get smaller deviations depending on reckoning with or without decimal cuts.

These values are obvious DEFINITIONS of the Petrie measured values — or CAN be understood as such.

— We can most freely use any of them, Petrie measures or those via the rJCIRCLE complex.

— They give the same result anyway — within the Petrie given measuring tolerances.

The previously given two SIO and yBlimit 19th course floor coupling descending floor quantities lead to a rJCR¦b16 definition of

THE PETRIE ESTABLISHED CORRESPONDING MEASURING B- point:

The decisive B-point is the place from where Petrie unites the descending tunnel with the ascending one, leading further south up to the named Grand Gallery and the two chambers.

— As the Petrie measures in this expedition by all means are LEADS and HINTS to a SIMPLE construction plan, if at all, the remaining is/becomes more or less ”a walk in the park” — provided familiar with TNED. See 18 in explicit unless already familiar.

Petrie B point: See also COMPLEMENTARY in yConCompl.

This FIT suggests that the constructors of the Cheops Pyramid had TOOLS with some extraordinary today obviously unknown capacity in executing extremely high precision constructs from prepared huge pieces of (cut) rock.

— Practically »no tolerance at all». The building has been standing there a long time along with earth quakes, obviously taking not too much hurt in suggesting silly tips, leads and hints of how it came about.

Approved:

— The Petrie decisive measuring B point is rJCR¦b16 defined.

— What is so special about ”the number 18”? FullAnswer.

SEE THE NOW (Jan2020) AVAILABLE ENGLISH VERSION OF A GENERAL OVERVIEW OF THE CONTENT IN UNIVERSE HISTORY here in NatCH.

— It’s all about mathematical physics in electricity, magnetism, induction and gravitation: nuclear physics at the level of absolute highest possible precision. We deal with all the fundamental most important parts with examples, quotes, comparisons, references and critical evaluations and aspects where possible: Faulty statements are NOT allowed here. The overall mission is: EXPLANATION. Zero speculations. We expose all the thorough DEDUCED connections, and explain how they are derived and how they connect to the absolute basic physics and mathematics — or not at all. The reader is the judge. Always has been.

We continue.

TheSeal: ThePush 1 ¦ ThePush 2

The Petrie Ascending Angles

HOW THE CONSTRUCT BECOMES »SEALED»

A sealing property appears directly through THE TWO PYRAMID AGENTS

THE rJCR¦b16 base offset 21.68’’ PUSH:

Having now determined all the basic inner design quantitative Petrie value corresponding measuring points

entrance passage tunnel G H B A coordinate points with

Pangle and Hangle, all the constructive layout properties connected to the ENTER entrance (nothing here mentioned on the two chambers except in R-multiples),

»it’s time to SEAL the package»:

— This author TAKES »the constructor’s role» to explain the details WHEREAS these already are obvious (or, if faulty, this author has some serious issues):

— With

the established GS-body pyramid agents rJCR¦b16 and PetrieCR¦b58 and the quantities we have derived and deduced from them and their actual mutual xy pyramid offset values

The offset values vertical-h horizontal-b between

the two pyramid agents PetrieCR¦b58 and rJCR¦b16

we (find — can relate — a corresponding geometrical, not actual physical) PUSH

the PetrieCR and its corresponding PetrieCP into the rJC¦b16 agents Acquired values.

Meaning as obvious:

impossible to deduce except through a corresponding TNED rJCIRCLE knowledge

— No PhD whatsoever or any body else in this or any other Universe will have a slightest smallest tiniest itty, bitty, tiny chance of DEDUCING the Edifice from a Golden Section Paragon geometrical Mathematica structure UNLESS acquainted with (a corresponding) TNED: THE DEDUCTION OF THE ATOMIC NUCLEUS → The rJCIRCLE: max neutron density.

— And what, exactly, would be the point in that?

Very Educated Population these days, big wall TV and the kind .. dying trees ..

School Student’s favorite subject: mathematics. MustBuyBook. Joy everywhere.

— Maybe we will find a brilliant answer in Natural Tenderness.

Returning to the building: The Device.

— IT has (now, as explained) become SEALED — granted protection from inspection, unless so understood — until TIME would come with a revelation: someone willing and motivated enough to dig for better answers than those coming from modern quarters.

Feel free to argue — knowledge to all for free.

ThePush1: PetrieBpoint ¦ TeSeal ¦ xBPetrieContracted — See lead illustration in BPOINTmain

PART I OF THE SEALING PUSH

THE VERTICAL HEIGHT of the ENTRANCE PASSAGE

THE ACTUAL Pyramid CONSTRUCTED Petrie measured QUANTITY

The two pyramid agents b1 and b2

— b1 as the rJCIRCLE Cheops Rectangle (CR) agent rJCR¦b16 and

— b2 as the actual Cheops Pyramid Cheops Rectangle agent PetrieCR¦b58

compose a delicate quantitative geometrical bOFFSET=21.67’’ horizontal PUSH.

— The PUSH is centered in the junction between the descending and the ascending passages in point B.

— The two pyramid agents horizontal push into each others quantities exposes a SET of perfectly defined CONSTANTS leading to a definition of the Petrie measured — and discovered — pyramid casing principle (Petrie19thProof): The Pyramid Casing Connection to the descending passage from the casing entering point.

— See also from ENTER.

Contracted by the two pyramid agents mutual half pyramid base quantity, the two sets ideally share one and the same descending roof. Useful Quantities are generated from that position.

THE ACTUAL HORIZONTAL OFFSET CONTRACTION between the two agents is illustrated as above, with a more detailed description below.

— We (now, finally) DIRECTLY understand why and how it is IMPOSSIBLE to deduce or even ”find” any PLAN for the building — UNLESS the two agents are discovered:

— Their ROLE, function and precise quantities.

These showed up through the simple rJCIRCLE complex introducing test (Nov2017) which soon unveiled the whole secret. And it has, since by further deduction, contributed to a profoundly clarifying picture of the whole edificial plan.

— Flinders Petrie and his 1883 measuring working group is responsible for this discovery. No doubt. See further TCA.

Detailed TP1:

In projecting the two pyramid agencies IN THE B-POINT REGION

on the

rJCR¦b16 b-value .............. 4555.88’’ offset in-push 21.68’’ relative the

PetrieCR¦b58 b-value ...... 4534.20,

including the Petrie given measures in the same B-region

+ 43.37 ......... = yATH

+ 4.11 ........... = yBlimit = yConB + yConBoffset = yConHBALimit = yConB + SIO

+ 3.57 ........... = BUARM

+ 1.84 ........... = [ bOFFSET — 18 ] / 2 = xB¦Petrie — xB — bOFFSET — 18

———————

= 52.89

/√1.25

= 47.31

bOFFSET — 18 = [xB¦rJ=1499.7016293661] — [xBPetrie¦rJ = xB¦rJ+18=1517.7] — bOFS] = bOFS — 18 = xBPetrieContracted.

it seems directly obvious (in this illustrative 10 inch scale) that they

the PetrieCP values and

the JCR¦b16 values

share one and the same tunnel roof of The Descending Passage. Exactly.

B Contracted Set A:

We — obviously — need to relate these details thoroughly unless we prefer to idealize — invite — some less shiny suggestions from Trouble Understanding Concept Enterprises: it IS old.

B Contracted Set B:

These two figures above and below show complementary different denotations used in this deducing part and its development (ATH: Ascending Tunnel Height; BUARM: B-point UpperAscendingROOF Averaged MEAN).

B Contracted Set C:

Especially in concern of the precise quantities, the illustration (TransPond) below explains — proves/exposes — some of the profound ideation behind the construct: how constants in the lower (B point) part are reused in defining constructing properties belonging to the upper (Gallery) part.

— R = (5^½ — 1)/2 = 0.618033988.., here The Golden Section Relational Constant. See also The ArcTan½: everything in the Golden Section Cheops Rectangle (Cheops Pyramid) construct plan connects to its simple right angle triangle.

Transposition Equivalent:

The figures below show the separate PLAN from the rJCIRCLE complex, left, and part of the actual physical Cheops Pyramid CONSTRUCT from Petrie’s values, right.

The PUSH-contracted parts: PLAN and Construct

The two above parts are shown complementary more in detail as actually horizontally contracted by the pyramid ½ side pyramid agents offset 21.68’’. That contract gives a resulting set of profoundly vertical exact constants leading to the definition of the 19th course masonry thickness as measures by Petrie. See the reckoning below from Summing Parts.

TheVerticalTunnelSum: ThePUSH1 ¦ Add1.84

An additional addend ADD1.84 appears through the horizontal offset between the two sets as bOFFSET — 18 = 3.68’’. Through the ArcTan½ triangle, the y value is half that: 1.84’’. The sum of the parts are then given below as above.

— SEEN FROM THE composite b-OFFSETED 21.68’’ horizontally CONTRACTED PETRIE B-POINT (blue): ITS VERTICAL (c) DELIMITS A tunnel vertical SUMMING OF THE PARTS

c = yATH + yBlimit + BUARM + (bOFFSET — 18)/2.

— And there can be no doubt about that, as seen: Just a contracted bOFFSET push to receive a vertical tunnel sum.

— We can test this by quantity in comparing Petrie’s value for the passage vertical height

— Petrie’s suggested ”19th course projective principle” says that this height value is the same as the horizontal thickness or height of the 19th stone block staircase masonry course (at the entrance level) —

as we now anyway have calculated all the decisive points at the site.

SummingParts:

— SUMMING UP THE PARTS as illustrated we find the vertical roof-floor rJCR¦b16 calculated quantity at the B-region with the rJCR¦b16 defined Petrie values included, as recently deduced;

— We arrive at the ideal Cheops Rectangle Golden Section Math ArcTan½ tunnel slope the related sum

c = yATH + yBlimit + BUARM + (bOFFSET — 18)/2 ;

c = 43.37 + 4.11 +3.57 + 1.84 = 52.89’’; paralleling this value gives the shortest tunnel normal

(52.89)/(1.25)^½ = 47.31’’ (47.3054871141)

If everything fits now, this value MUST — irrevocably with no tolerance — connect to Petrie’s measured 19th floor height (668.2’’ ± 0.1) as calculated by our EXACT rJCR¦b16 agency values:

— It must define the Petrie given values.

And it SO does.

The results as presented in OpenOffice calCard (conv. spread sheet : what farmers use for harvesting oats):

Proving he Petrie 19th floor arithmetics: See also cSIDE illustration

The D-form below is the same as used in yConBoffset and Add1.84.

ENTER ¦ MainConstruct ¦ SummingParts ¦ ThePush

FOR PREFIXxSIN, SEE TRIGREF unless already familiar.

PREFIXxSIN ¦ R ¦ PetrieCPm

D = 37.9657350065’’ = 19th course height at entrance:

— And it so does: 37.94’’ ± 0.17 ¦ 47.30’’ .......................... approved

yBarm ILLUSTRATION ¦ TP1Det ¦ SIO

([yATH + yBlimit + Buarm + (bOFFSET — 18)/2]/√1.25)cos(ArcSinR)/cos(ArcTan½ + ArcSinR) = 37.9657350065’’;

— Descending tunnel: √1.25 transforms vertical to tunnel parallel in the ArcTan½ triangle. 2R = √5 — 1.

” The crucial test then is, supposing the passage prolonged outwards till it intersects this course, how will its end, and the face of the casing, stand to the casing stones at the foot of the Pyramid? The answer has been already given in the list of determinations of the casing angle. It requires an angle of slope of

51° 53' 20" ± 1' ”, PetrieCH6.32.

” Mean axis of whole length ¦ Altitude

26° 31' 23" ± 5" ? ”, PetrieCH7.36eTab.

The fact that Petrie used his (idea of a) casing surface by his staircase masonry measured angle

51° 53' 20" = 51+1/1.125 = 51.8888..° OBVIOUSLY

does not affect the end result

19th course height 37.97’’ (Petrie 37.96’’¦37.94’’ ±0.17)

on the IDEAL Cheops Rectangle Golden Section paragon Cheops Pyramid’s (PREFIXxSIN) casing end angle

ArcSinR = ArcCot√R = 51° 49’ 38.25’’ = 51.82729238°:

— The construction/paragon OBVIOUSLY includes both.

Quantities approved.

CONCLUSION:

— There seems to be no way in refuting a general idea that the ideal Cheops Rectangle Golden Section paragon mathematics through the rJCR¦b16 agent in general DEFINES the whole Cheops Pyramid building — through the Petrie measured values.

— We find, as of yet, no actual opposition to that conclusion — still looking for one.

ThePush2: TeP1

PART II OF THE SEALING PUSH

THE GALLERY ANGLES

THE ACTUAL Pyramid CONSTRUCTED Petrie measured QUANTITY

In calculating [BUARM] the location of the Petrie measured [1658.2’’][pGconBuarm]

Gallery PG-point

1658.17’’ = yPG

ArcTan½-math: ......................... (b1 + b1xB)/2 + b1yB — [yBarm = yATH + (BUARM=GSintersectionDiff)]

= 1658.1652607385’’ .............. rJCR¦b16 = b1

through the main ArcTan½ Golden Section paragon geometrical mathematics,

that ArcTan½ based result WILL become exactly so certified as

a definite property of the rJCIRCLE agent rJCR¦b16 character:

TP2.1: TeP2

REALIZING THE PUSH to acquire the 21.68’’shorter

Petrie Cheops Pyramid ½ Petrie measured base

PetrieCP¦b = 4534.4’’ ± 0.25

PetrieCR¦b58 = 4534.20’’ ± 0.000 = 58R√16000 = 4534.196576’’

TP2.2: TeP2

we have arrived at a s(i)t(u)ation where ANOTHER inner design CONSTRUCT PLAN will be necessary, due to the so Golden Section paragon rJCR¦b16 breach:

TP2.3: TeP2 ¦ ConAnLi ¦

— The rJCR¦yB point — situated over the yBlow PG rJCIRCLE agent calculated reference — must now take a leading constructive position to the layout. Namely on a higher (yB over yBlow) reference to the former master PG — as »a slave pG».

— This leads the construction plan into a corresponding basic (absolute) lowest possible ascending floor construction angle pG→yB of the value 26° 1’ 3’’:

The pG→yB = (minimum) construction angle for an ascending (B→pG) passage then:

ArcTan(ypG — yB)/(xpG — xB) =

= ArcTan(yPG — yB)/(xPG — xB — bOFFSET)

= ArcTan(1658.17—177.02)/(4555.88—1499.70 — 21.68) with calCard rJCR¦b16 decimals

= ArcTan(0.4881106914)

= 26.0174979947°

= 26° 01’ 02.99 27 81’’

Condition:

26° 1’ 3’’ = ConAnLi ........................ absolute lowest floor angle construction limit

— As the real physical Petrie (blue above) B-point is

vertically y-situated below the master rJCIRCLE Golden Section paragon yB- point

we SHOULD find no smaller measured values in the corridors and tunnels from Petrie’s expedition on the ascending slope — in order to keep the construction maximum tight, without »vacillating around»;

— In Quote PetrieCH7.37 Col3 from Row1 — the angular values on rows 14¦16¦19¦26¦45¦46.

We will soon return to this specific part

(proving a reckoning of exact Petrie corresponding reference angles, further below — with a safe GS body rJCIRCLE connection).

— First a few GS-observations on the Petrie mentioned ”plugged part”.

PlugBlockPart: See Petrie details in The Measured

The Plugged Part — short

The ”plugged part” (xSouthPP) mentioned by Petrie, its south end, is directly identified (checked through Petries values) from the Cheops Rectangle Golden Section paragon situated horizontally south from the Pyramid’s north base at

xSouthPP = P4 + PiLINE = b·R^[4—1] / √5 + b·R/ √5 ; b=4534.20’’ = rJCR¦b58:

= (b/√5)(R^3 + R) = 1731.91’’ ;

Length from yB:

— (xB=1499.70) = 232.21’’

— (Lower offset PetrieCH7.38: 50.76’’)/√1.25 = 45.4’’

= 186.81’’ / 12 = 15.57 feet horizontally = 4.744974 M.

”.. the large plugs of granite that fill some 15 feet of its lower part ..”, PetrieCH7.38.

VALUES CALCULATED FROM THE PYRAMID AGENT rJCR¦b16

FUNCTION (my reflexion): Without a HARD (conically shaped, tight fit) plug, the above pushing stone masses would have shredded the tunnel by time and many small earth quakes. Result from That Knowing: The Plug was directly added At The Horizontal Construction Site for stability and minimum stress.

— Additional reflexion: Who made this geometry? The GS-paragon is a geometrical structure LIKE Pythagoras Theorem. It has no constructor. It is a natural property inside geometry: nature stuff — monumented by humans: obviously to guide later Eventual suck-ups on the right path: Proving an early familiarity. A Monumental Edifice.

— »Occupied by later less educated suck-ups».

TP2.4: TeP2

Returning (From TP2.3) to The Push:

By consequential constructive purposes — angle by pG→yB marks the upper limit — the constructing ascending floor angle slope will hence receive The Petrie B-point B’ as a physical »Lower Floor BEGINs Here» reference — exactly coherent concordant, as measured by Petrie.

As the Petrie B’ point is xy situated south drawn below the ordinary rJCR B point by (18.00;4.11)’’, Petrie will — or should according to our explaining test — measure a slightly greater angle than the above calculated absolute angle minimum 26° 1’ 3’’:

Namely (exactly)

PetrieCP:

Tan pGB’ = (1658.2 — 172.9)/(4534.4 — 1517.8)

pGB’ = 26.2145061252° = 26° 12’ 52.22 20 51’’

PetrieCR: With directly Petrie-compatible R-multiples — where available:

Tan pGB’ = ([2683R]=1658.185192 — [yB’=280R=173.0495169])/(4534.1965759686 — [xB’=2456R=1517.891476])

pGB’ = 26.2142137518° = 26°12’ 51.16 95 06’’

— PetrieCH7.39:

” This, when corrected for lower signal being 3 too high, gives

26° 12' 50" for mean angle of both passage and gallery together. Hence, from my offsets to the places of these signals, the absolute angle, and the variations from it, can be obtained for either part independently.”

Approved: The values are practically one and the same.

— I believe this angular line pG→B’ is what PetrieCH7.45 calls ”the virtual floor”: it is lying above the actual physical floor as a pure sight-line where the actual physical floor is being BENT

” which is bent on passing from the passage to the gallery”

in a (very small) two angle breach at the beginning of the lower North Grand Galley wall (same level as the tunnel floor entrance to the Queens Chamber).

— THAT seems definitely VERY complicated. Is there a rJCIRCLE GS-body connection?

— It better be. We study that possibility.

TP2.5: TeP2

The Petrie ”virtual” 26° 21’ 50’’ angle will not do as a final constructed physical floor slope.

— Why is that?

SHORT REPETITION: The PUSH has breached the basic rJCR¦b16 GS-body paragon layout: IT will NOT be found as such inside the corresponding actual ideal Petrie Cheops Rectangle pyramid PetrieCR¦b58 — unless some (sophisticated, adopted) adjustment (in the layout) is made.

IF our explaining construction plan is going to hold

— all physically constructed floor angle parts must lie within the angle sector pG.yB.B’

— then the green lower parallel to the dotted line pG→yB will mark an absolute physical floor lower construction limit: it is NOT violated IF our test survives.

— »Petrie shall NOT find an angular value breaching this condition».

— Where do we find the reference points for such a highly advanced enterprise?

LATEST MODERN NEWS [Jan2020]:

— »The Egyptian Workers were psychic, says modern academic archaeological scholars».

— »’They knew exactly where to put it’, says PhD Walcome Modern to Latest News».

Taking a lead from the original rJCR¦b16 position:

TP2.6: TeP2

— THE SEARCH FOR GALLERY NORTH:

a: The GS-body paragon used for taking The Aline parameters to the intersecting point in the LOWER calculated values.

b: Enlarged view of the Aline on the inner Cheops Pyramid design. The UPPER part — see the BUARM calculation — is not used here in explicit.

c: The GS-body paragon used for taking The Bline parameters.

d: Enlarged view of the Bline on the inner Cheops Pyramid design.

The values above from the (terrible but free OpenOffice) calCard

expose ”a rough average” to — but still far from — the Petrie measured corresponding »EXACT» values:

— PetriCH7.39:

”These, added to previous amounts, give for the absolute place of the floor end at the latitude of the E. wall of the gallery

(172.9 + 679.7) =

852.6 ± 3 level above pavement;

(1517.8 + 1389.5) =

2907.3 ± .6 horizontally from N. edge of Pyramid, or

1626.8 ± .8 northwards from centre; and 287 ± 1.5 for middle of passage eastward from centre of Pyramid.”.

NOTE: Petrie’s figure ± 3 in ”852.6 ± 3” is — probably, most likely — a print error:

— In PetriCH7.40tab he writes (here assumed the more correct ± 0.3)

852.6 ±.3 ¦ Mean doorway on floor

We will take it further on that ± 0.3 part:

By further consequence and (exact) proof:

— We concentrate only on the LOWER intersection part:

• At First: We test — certify — that these values, the actual intersecting point xyA¦B,

lie OUTSIDE the recently stated angular limit (TP2.3¦ 26° 1’ 3’’) in the triangle area pG.yB.B’:

— If, namely, the point would be inside ConAnLi we would have no reason to continue the search.

— So: How do we do The Test?

— As we already have the xy coordinates, we (simply) take the xyA¦B point from the Petrie B’ point — our rJCR¦b16 calculated EXACT construction spouse, of course — which directly gives us a comparing angular value (absolute xy values only):

Referred [linked sections] values — all values below in INCHES:

XLoBnom = LowerBlineNOM ....... =

XLoAnom = LowerAlineNOM ...... = b — P

xyAB = intersection point from LineAB, see Intersection Math unless already familiar.

— We directly see that this value 25° 34’ 10’’ is out of hand and range: something (radical) must be done here to make the construction fit within the (here, still at test) 26° 1’ 3’’ConAnLi preference.

• At Second: We directly onset the pushing bO = 21.68’’ bOFFSET (TP1¦TP2) to the above nominal rJCR¦b16 values: we keep these, and just modify them horizontally x-ways with the bOFFSET addition — plus eventually other near associates (OFK=18 and S=100R are always close Golden Section Cheops Rectangle rJCIRCLE candidates);

— We continue (bOFFSET = bO):

— We still have some work to do here: 25° 55’ 05 is to short. We must get over 26° 1’ 3’’.

The end result:

The Petrie D-point: TP26

— This makes it — within Petrie’s given tolerances:

——————————————————————————————————————————————————————————

RECT — SPIR ¦ xLoAnom ¦ xLoBnom ¦ PetrieCH7.39Quote ¦ bO ¦ 18 ¦ R

Defined — as so within the Petrie specified tolerance limits.

The Golden Section paragon mathematical geometry truly seems to defend a close connection to The Foundation of a physical Construction Plan for The Great Cheops Pyramid.

The resulting rJCR¦b16 calculated angles related to point D is illustrated below in an exaggerated angular illustration to clarify the details.

TP2.7: TeP2 ¦ OFK ¦ bOFFSET ¦ ConAnLi ¦ yBlimit ¦ pG

EXAGGERATED ANGLES FOR CLARIFYING DETAILS

The D.B’ angle VIOLET low part DOTTED is truly slightly larger than the pG-B angle GREY DOTTED: The Violet 26° 3’ should have been positioned between the gray 26° 1’ and the blue 26° 12’. However to give a view on the D-point, an illustrative violation is made here in pushing D outside the allowed, making us »a split vision geometrical view» of the whole complex. The values below are the true angular values as calculated in the following tables. The top VIOLET Gallery part parallel to D.B’ will be discussed further [‡], included here only for reference.

The R-designation on top [and associated] row gives the corresponding Within-Petrie-Tolerance whole number R-multiple [WRM], if at all, 2 decimal rounded. The Petrie D-point xy coordinates as calculated and Petrie given:

PDang: TP27

The compiled calCard calculated angular values associated with Petrie’s D-point:

TheLostAngle: PDang

Petrie’s ”signal to signal” In Quote Row30 PetrieCH7.39.

”Signal” — 1883? Not with any Transistors anyway.

Measuring (solid, geodesic, trigonometric, theodolitic) reference points.

— The only known TRIGONOMETRIC way to understand Petrie’s description In Quote Row30 PetrieCH7.39 is (TP27) as seen from the Petrie D-point:

The distance E.(CB) or its end angles can be calculated

only if the distances D.(CB) and D.E are known together with their respectively angles.

— However, apart from the quoted PetrieSignal section:

— Petrie gives no (direct) information on WHERE his ”signal” were situated, especially at the south Gallery end — except In Quote Col1 ¦ Row26 PetrieCH7.46 the additional information in PetrieGallery.

— PetrieCH7.39 ¦ Col2 ¦ Row11: ”the sloping length of the passage being 1546.8’’.

SPECIAL TRIGONOMETRIC TRIANGULAR CONNECTIONS:

In PREFIXxSIN: b = E→B = (ac[a/c + c/a — 2sinF])^½ :

c = D→B 1546.8’’ ”from beginning of ascending passage”

(D.B)° 26° 2' 30" In Quote PetrieCH7.38 Col3 Row14

a = D→E 1815.5’’ In Quote PetrieCH7.45 Col2 Row13

(D.E)° not connected, missing data

b = E→B cannot be calculated without a (D.E)°

(E.B)° cannot be calculated without a (D.E)°

F° = 180° — (D.E)° + (D.B)°

THAT IS TO SAY:

No angular value

— only a distance value ”Ramp end 1815.5”

— is mentioned between the reference points D and E (pG)

— ”.. but we can obtain the angle of slope very satisfactorily, by taking the angles observed to signal at bottom of ascending [p. 65] passage, and to signal at top of gallery, and then (knowing the distances of these signals) calculate the angle of slope from signal to signal”, PetrieSignal Row25.

From where did Petrie get a (D.E)° value?

— He mentions no value.

What (D.E)° angle?

We can test this precisely with our rJCR¦b16 exact mathematical GS-body geometry in comparing the other Petrie given values on the lower Gallery part (Petrie D point) of »The Petrie Queen Site expedition»:

— As is evidently shown in the Petrie D point section, the acquired corresponding rJCIRCLE complex values lie within the Petrie given tolerances:

Not mentioned by Petrie, only suggested:

PetrieCH7 accounts for »a general method» in calculating the mean Gallery floor slope from known angles and lengths by his ”signal to signal” (In Quote PetrieCH7.39 Row30).

PetrieCH7.38 In Quote Col2 Row11 specifies length

D→B’= 1546.8 on angle 26° 2' 30" In Quote PetrieCH7.38 Col3 Row14:

”.. The angle of the whole passage will be discussed further on; it will suffice to say here that the mean angle is 26° 2' 30"; and there is therefore a presumption that the plugged part is about the same angle”.

— PetrieCH7.45tab In Quote Col2 Row14 specifies a ”Ramp end ¦ Distance on slope 1815.5” as (crosscheck by trigonometric calc.) Length D→pG¦E.

The D.E angle (PetrieCP¦pGD):

But Petrie gives no actual angular value

(calculated PDang as above 26° 20’ 26.36 27 56’’)

for this length D→pG

(neither a value of ” 20’ ” exists in the text, and nor any ”19’ ” — A lowest Petrie 1658.2±0.6=1657.6 gives a 26° 19’ .. But neither such a figure is mentioned in Petrie’s text;

— As we, here, rely on this indirect Petrie 1658 figure, we really have no detailed clue in how Petrie reached his top slope gallery step face level value as mentioned

In Quote PetrieCH7.46 Col1 Row40, the figure

1689.0 ± 0.5 [with an explained additional measured + 4.16 = (1693.16 ± 0.6 → nom1693.2)]).

xy-difference: ±0.6’’¦0.08’’; ± 0.3’’¦0.22’’

PetrieCH7.39 values: responding rJ calculated:

xD = 2907.3’’ ± 0.6 2907.38’’ ¦ 2907.3786302

yD = 852.6’’ ± 0.3 852.82’’ ¦ 852.8245796

———————————————————————————————————————————————————————

”These, added to previous amounts, give for the absolute place of the floor end at the latitude of the E. wall of the gallery

(172.9 + 679.7) =

852.6 ± 3 level above pavement;

(1517.8 + 1389.5) =

2907.3 ± .6 horizontally from N. edge of Pyramid, or

1626.8 ± .8 northwards from centre; and

287 ± 1.5 for middle of passage eastward from centre of Pyramid.”, PetrieCH7.39.

———————————————————————————————————————————————————————

— The D.E angle with nominal values from Petrie1658:

Tan(D.E)° = (yPG—yD)/([xPG=bPetrie=4534.4]—xD)

(D.E)° = ARCTAN (1658.2 — 852.6)/(4534.4 — 2907.3)

= 26.3406563211° = 26° 20’ 26.36 27 56’’

— The trigonometric formula for the Petrie reasoning ”signal to signal” method,

In Quote PetrieCH7.39 Row30

demands (2 sides, 1 summing angle: from reference point D)

knowledge of both lengths:

— The downwards descending

c = D→B’ = 1546.8’’ and the PetrieCH7.45tab upwards ascending

a = D→pG¦E = 1815.5’’ and their angles

F° = 180°

— Upper° = 26.3406563211 = 26° 20’ 26.36 27 56’’ ...... our HelpPetrie missing calculated DEangle.

+ Lower° = 26.0416666666 = 26° 02’ 30.00 00 00’’ ....... Petrie’s nominal In Quote PetrieCH7.38 Col3 Row14

= 179.701°

PetrieBE: FourGiven ¦ DEangle ¦ The Lost Angle

THEN WITH a GIVEN — COMPLETING THE PETRIE MISSING INFO — WE CAN FINISH ON WHAT PETRIE MUST HAVE COMPLETED: THE b SIDE FROM acF°, AND THEN FINALLY THE yPG FROM THE PYTHAGOREAN FORM WITH b AND xyB.

Most simple (we calculate distance b = pG→B’ from The four given):

In PREFIXxSIN:

b = pG→B’ = (ac[a/c + c/a — 2sinF])^½ =

= 3362.2886273723’’. The b-angle: ArcSine (4534.4-1517.8)/b =

b° = 26.2093239122° = 26° 12’ 33.56 60 84’’

(Petrie’s 26° 12½’ angle in CH7.38 ”.. and 26° 12½ ' as the ascending angle”).

The horizontally b-projected length (b·sinb°):

xb = 3016.6’’ ............ PetrieCH7.64tab results also specifies 4534.4—1517.8=3016.6 [Table error 3016.3];

compared to the alternative Petrie given (½Pyramidbase=4534.4) — (xB=1517.8) =

xb = 3016.6’’ — Same value.

PetrieIndirectlyVerified1658: STRONGLY EXAGGERATED ANGLES FOR CLARITY — PetrieBE

The resulting vertical pG-point height from the trig-form:

The Pythagorean form with recent designations:

√[(b=3362.2886273723)² — [(½PetrieCheopsPyramidBaseb=4534.4) — (xBPetrie=1517.8)]²]

+ (yBPetrie=172.9) =

ypG = 1657.8610276897’’ ~ 1657.86 compared to (the indirectly Petrie1658 summed)

yPG = 1658.2’’ ± 0.6, lowest 1657.6. Nominal Difference: 1658.2—1657.86 = 0.34.

— Approved and verified.

These Petrie cross checking tested calculations (initially and necessarily [perhaps] made by Petrie from 1883) only confirm the correspondences on the Petrie (indirectly calculated) Gallery top sloping floor pG-point — however never explicitly mentioned by Petrie himself. See QuotePetri1658.

We see — for comparing clarity — that the Petrie given nominal values have small (discernible) deviating figures from other slight different numbers WITHIN the Petrie given tolerances. The PDang calCARD above exposes this explicitly on the first top row, same within-tolerance figures: Petrie’s part at the right and the rJCR¦b16 calculated to the left, same (Petrie tolerance) approved D point.

PetrieDAngles: TP27

Petrie on the D-associated angles 26° (2-7)’¦26° 12’¦26° 20’

— See In Quote Col3 PetrieCH7.38.

— See also The Plugged Part.

— Petrie mentions the D-point associated angular uncertainty part in

PetrieCH7.37:

” The surfaces are so much decayed and exfoliated, that it is only just at the ends that two original faces can be found opposite to one another; hence the width and height cannot be measured, and the offsets can only be stated to one surface.

From this altitude, the sloping length of the passage being

1546.8, the horizontal length will be

1389.5, and the vertical height

679.7, both being corrected for difference in the offsets of the ends.

The determination of the azimuth has, unhappily, a large probable error,

± 3' (owing to bad foundation for the theodolite in Mamun's Hole); and its direction,

– 4', is so close to that of the Pyramid side, that it may be assumed parallel to that

± 3'. This, on the passage length, =

1.2 inches for the probable error of the place of the upper end of the passage, in E. to W. direction in the Pyramid.”.

Calculating example from Petrie’s values — showing the relative errors:

PREFIXxSIN:

ArcSin(1389.5/1546.8) = ............... 26° 3’ 49.29’’

ArcCos(679.7/1546.8) = ................ 26° 4’ 1.53’’

ArcTan(679.7/1389.5) = ............... 26° 3’ 59.17’’

These values compared with the previous, top row

Petrie CP¦DB’: .......

ARCTAN (852.6 - 172.9)/(2907.3 - 1517.8) =

= 26° 3’ 59.17 05 23’’ ←

b16compar.: ..........

ARCTAN (852.8245796 — [177.0157652488 — 4.1112567233])/(2907.3786302 — [1499.7016293661 + 18] =

= 26° 4’ 15.15 74 46’’

show that ”the exact” internal Petrie preference here is of the TANGENT type — same DMS (DegreesMinutesSeconds) figures — While the ArcCos-part is more close to the rJCR¦b16 calculated part.

— In any of the ways, we see that these Petrie given METRIC figures lie within his given tolerances.

So:

— Any of these values will find an approved recognition.

The corresponding PetrieCR¦b58 has no known match

An interesting parallel:

— What (corresponding) values are given by the PetrieCR¦b58 part?

— Not good: The RECT(type:—5.85) and SPIR(Type:+24.7) have to be pushed in opposite horizontal directions for a corresponding Petrie approving near xyD 2907.36; 852.76. That is obviously, as we know, not our table: no known correspondence. It is all about the rJCIRCLE part.

— Calling ATLANTIS .. ello .. ello .. 222 .. 333 .. ¦ ATLANTIS ¦ GTursprunget2019 ¦ AtlantisAPPENDIX ¦

— Roger .. Roger .. Mayday .. Mayday .. A GEOATLANTIS seems to be capable in EXPLAINING else-way enigmatic GLACIATION VARIATIONS — reported only over the NORTHERN HEMISPHERE.

DESCENDING PASSAGE LowHighMEAN:

Finding the most direct and simple adopted exact quantities from the Golden Section paragon mathematical geometry

DESCENDING PASSAGE LowHighMEAN

by rJCR¦b16 = 4555.88’’

The Descending Passage DP vertical height

— testing quantity matches to the 1883 Flinders Petrie Cheops Pyramid measurements

We have two independent ways leading to the same result.

— The illustration’s left part shows the two most obvious visual fittings for the GS-body on the Petrie measured inner design of the Cheops Pyramid. We see (by magnification, see on top) that the leftmost dpLOW candidate exposes a slight lower paragon fit than the middle dpHIGH one.

— Allowing only use of the GS-body’s definite geometrical quantities the above illustrated math conditions appear:

— The difference in vertical height between dpLOW¦y and dpHIGH¦y becomes

—(b — P/2 — (2b — Gx)/2) + Gy = |1184.04|’’ — |1092.18|’’ =

91.86’’ with rJCR¦b16 = 4555.88’’ ;

The mean vertical (y) difference between the the two is

(dpHIGH — dpLOW)/2 = [—1092.18’’ + 1184.04’’ = 91.86’’]/2 =

45.93’’

See also general drawing metrics and calculated results more in detail in

Phase1RESULTpointG.

With respect to the actual construct (Petrie mentions ”a flat end”) at the end of the tunnel, Petrie gives two values:

PetrieCH7.37tab.

upper edge ............ 48.5’’

lower edge ............. 38.3’’

Extracted @Internet SEE The PETRIE SOURCE for research purpose

— testing Petrie measured values against the GS-body mathematical geometric quantities: PROVING THE CONSTRUCT.

Comparing the Petrie values with the averages rJC¦CR-values have no visible representation to the naked eye in this illustrated scale (from PetriePLATE.9).

For the local rJCR-values, see Phase1RESULTpointG.

Whole number R-multiples:

WHOLE NUMBER R-multiples can be tested with Petrie’s given values and their tolerances — as it now already is clear (Background ¦ IntroEX) that the construct DID use such GS-paragon precision methods (and instrumentation).

EXAMPLES with multiple R

— confirmed by Petrie measured values

King’s Chamber midpoint:

Directly with S = 100R = 61.80’’:

S(7 + 1/100) = Kings Chamber Ceiling Midpoint from Pyramid vertical Centre:

433.24’’ = 433.2418261 = 701R;

— PetrieCH7.55e:

” The position of the King's Chamber in the Pyramid is defined thus:

N. wall at base

330.6 ± .8 S. of centre of Pyramid; S. wall

537.0 ± .8 from centre; .. ”

Check: (N¦330.6 + S¦537.0)/2 =

433.8 ± 0.8 ¦Low¦433.0; Hih¦434.6 ................... approved

NomDiff: 0.558.

Queen’s Series:

All the following Petrie given measuring series on the so called Queens Chamber have whole R-multiple quantities within the Petrie given tolerances:

QUEEN CHAMBER

PetrieCH7.40tab: ¦Floor level¦Theodolite measured ¦ R = (5^½ — 1)/2 = 0.618033998..

— The whole Petrie series of values approve:

OPEN OFFICE CalCARD.

The OK cell code: IF Difference >Tolerance THEN print ”notOK” else print ”OK”. OK means: approved. NoProblemo.

These value examples MAY seem »a little trivial»: The R-unit — R = (5^½ — 1)/2 = 0.681033988.. — is pretty much ”precisely” ± 0.3. On the other hand: »The Constructors counted on precisely that».

— Without speculation — speculative conclusions are not allowed here — we can neither prove nor refute these possibilities. It fits (any way).

QueenFloorIn:

Specifically we have the (vertically) Queen’s (partial) floor level

y = 1385·R = 855.9770744;

yQUEEN = 855.98’’ ¦ Petrie 856.2 ±.3 ¦On floor ...................... APPROVED

NomDiff: 0.222.

with the corresponding horizontally Petrie measured connecting point between the end of the Ascending passage — where it meets the beginning of the Grand Gallery, and the horizontal tunnel into the so called Queens Chamber, PetrieCH7.39:

” ..

(1517.8 + 1389.5) =

2907.3 ± .6 horizontally from N. edge of Pyramid, or

1626.8 ± .8 northwards from centre; and 287 ± 1.5 for middle of passage eastward from centre of Pyramid.”

x = 4704 R = 2907.231883 ~

2907.23’’ ¦ ........................................................................................... APPROVED

NomDiff: 0.002.

And further.

— Calling ATLANTIS .. ello .. ello .. 111 .. 333

— Roger .. Roger .. Mayday .. Mayday ..

CONCLUSIONS: What18: — OFK OFFSET FACTOR K ¦ The ±e-mass quantity responsible for all atomic masses as defined in TNED ¦ — Compiled for UD Jan2020 —

WHAT 18? See also in The MiUNIT.

— As already noted: Not much in this presentation is known in modern academic quarters.

Construction basics as proved

FLOOR 19 AND ROOF 18 ¦ Proving the 19th Floor — rJCIRCLE complex connection to Cheops Pyramid

— All most essentially and universally connected to ELEMENTARY atomic and nuclear physics.

— See WHAT18 a (shorter) detailed description in (CheopsAtlantisTNED), unless WHAT18 already familiar.

MiUnitIntro: THE CHEOPS UNIT S = 100R

MiUNITbasic ¦ The MiUNIT ¦ MiUNIITcomparingTable

The MiUNIT — INTRODUCTION, How it was observed [Nov2017], see KingILLUSTRATION.

— The Pyramid half square Base (b) multiplied in succession by the Golden Section Constant R = (5^½ — 1)/2

as in b·R^n with n from 0 and up gives — with rounded two decimals — on n=18 the value 1.27 — which is 2.54/2.

— See these values in Table @ExactComparingBasics.

— We can use Petrie’s Cheops Pyramid [CP] measure

PetrieCP¦b = 4 534.40'' or the ideal 2 decimal ROUNDED Petrie Cheops Rectangle [CR]

PetrieCR¦b58 = 4534.20'' or the full decimal

PetrieCR¦b58 = 4534.196576 = 58R(16000)^½.

— All end on n=18 at 1.27.

— And there we go: The GS-body arithmetics contains a (Pyramid measuring basic) MeterInchUNIT of the form

0.0254 M = [ROUND 100·(2b·[1Meter/1Inch]/R)·R^18]/10000

= 1'' ;

2.54 = 2b/R · R^18

bReferences: The 2 pyramid b-agents ¦ GS arithmetics

See also the [b¦PnMAP] (Sw.orig.2017) bPetrieCheopsTable.

— The corresponding ideal GS-body geometrically EXACT PetrieCR¦b58 spouse 4534.20 tabled values are shown (here recalculated Jan2020) below:

— The Pyramid half square Base (b) multiplied successively by

R = (5^½ — 1)/2 as in b·R^n with n from 0 and up gives

— with rounded two decimals — on n=18 the value

1.27 — which is 2.54/2.

— We can use Petrie’s Cheops Pyramid measure

PetrieCP¦b =4 534.40'' or the ideal 2 decimal ROUNDED Petrie Cheops Rectangle

PetrieCR¦b58r = 4534.20'' or the full decimal

PetrieCR¦b58d = 4534.196576 = 58R(16000)^½.

— All end on the same n=18 @1.27.

— And what’s so special about 18? The Neutron — the rJCircle BASE. The whole complex — says TNED. »Central Nuclear number»:

— The Atomic Masses certifying that TNED + Experimental physics = True. THE NEUTRON SQUARE — unknown in MAC.

ExactComparingBasics, the MiUNIT:

Table extracted and recalculated and compiled here for comparing values from the original Swedish version 2017.

— ABBREVIATIONS and terms are detailed in HowStart — unless already familiar.

— All end on the same n=18 @1.27 = 2.54/2:

— We have found a (Pyramid measuring basic) MeterInchUNIT of the form

0.0254 M = [ROUND 100( 2b[1Meter/1Inch]/R)R^18]/10000

= 1''

1 Inch = 0.0254 Meter — standard electronics construction raster [10UNIT] for integrated circuits. Really.

— NOTE: 5·8 + 18 = 58. Really (»Advanced Alzheimers»). See The 1818+18+k Neutron.

— The Mi¦UNIT. The PETRIE¦Cheops Pyramid Unit [»The CU»]. Petrie and his working group — and the contributors who showed the parts — are responsible for this discovery (with some supporting interest from an accidentally passing by pedestrian ..).

The MiUNIT: MiUNITbasic ¦ FIRST APPEARANCE

COMPARE PetriCP and PetrieCR

The Mi¦UNIT — MeterInchUNIT ¦ 16 •18 • 58

R = Golden Section Constant (5^½ — 1)/2 = 0.618033988..¦ b, see bREFERENCES — Cheops Pyramid ¦ k0

With Petrie’s specified measure 61.7±0.8 inches from the Pyramid Centre (C-line), we can most freely with only a utilized tolerance of ± 0.15 adopt a (MeterInch-UNIT) in association with the 100R = 61.80’’ Petrie Cheops Pyramid Top Gallery value through the following exact corresponding arithmetics:

Petrie100Rsource: MiUNIT

PetrieCH7 mentions the

61.7 (± .8) value 5 times. We have 61.8 = 100R:

The Golden Section body Relational value

R = (5^½ — 1)/2 = 0.618033998.. has several direct WHOLE NUMBER R multiple quantitatively affirmed connections to the 1883 Flinders Petrie given Cheops Pyramid measured values — WITHIN Petrie’s specified tolerances.

Directly with S = 100R = 61.80’’ = CheopsPyramid UNIT (CPunit):

S(7 + 1/100) = Kings Chamber Ceiling Midpoint from Pyramid vertical Centre:

433.24’’;

— PetrieCH7.55e:

” The position of the King's Chamber in the Pyramid is defined thus:

N. wall at base

330.6 ± .8 S. of centre of Pyramid; S. wall

537.0 ± .8 from centre; .. ”

Check: (N¦330.6 + S¦537.0)/2 = 433.8 ± 0.8 ¦Low¦433.0; Hih¦434.6 ............. approved