CHEOPS ATLAS ¦ UNIVERSUMS HISTORIA | a production 2020I1 | Senast uppdaterade version: 2020-03-28 · Universums Historia

 

 

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

 

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=h˛. 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

 

   ENTERMiUNIT. 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 OVERVIEWThe 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 ArcTan˝ 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 ˝ 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 IntroEXR = [√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 deductionPART 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 ArcTan˝ 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.

c:

— 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 ˝(yG–yG’) nominal (2.8172301665) difference (The nValue) has an ArcTan˝ 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 deductionPART 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 + bOFFSET18 + 2yConB = 856.2949417436 ~ 856.3:

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

 

The bOFFSET18 part in explicit (it also connects to the yPonB part) is the horizontally contracted result of which vertical (ADD1.84) ArcTan˝ 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 deductionPART 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=h˛ 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 ArcTan˝! 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^˝ — 1)/2          Point A:                        FULLY PETRIE CERTIFIED CALCULATED QUANTITIES

unitINCHES                 rJCR internally calculated     formula/term

———————————       ————

Tunnels                        26° 33’ 54.18’’                        A° = ArcTan˝

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

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^˝ — 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^˝ — 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          yGnValue = 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 = ArcTan˝ – ArcTan(π/[AGdistance=4135.338346’’])

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

 

R = (5^˝ — 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 firstR = (5^˝ — 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 [yDyB-yBlimit]/[xDxB18]

*                                    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^˝ — 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

SEE ALSO IN  Introduction — SOME DETAILS ON THE OUTER FORM OF THE GREAT 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 ArcTan˝-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 ArcTan˝ 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 Petri 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 Petri 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 LawsThe 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=h˛ 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=h˛ 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 startedbasic 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/Mł.

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)˛+1] = 1.7159333294  = rJ/b ; b:=rJCR¦ b16=4555.88’’;

rJCR¦b16 ................     rJ/k0 = (100R√16000) / √[(2/√5 + 0.5)˛+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: Petri 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)˛+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=h˛ 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  ARITHMETICSArcTan˝LINE — The GS-bodyNatCH — The Golden Section Relation R = b/d = [√5 –1]/2 = 0.618033988:

 

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

 

Leftmost [R1↓, R˛ → , Rł↑, 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. Pärlbĺtssnäckan). 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 origoLatin: 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^˝ –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 ˇ 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 ArcTan˝ 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 ArcTan˝ 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 ¦ yConBUARMcalc.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 + yByBarm = 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 on The MiUNIT.

 

 

 

TGS: PETRIEpG — TheGalleryTES  — GalleryTop:

 

Cheops Pyramid data from Flinders Petrie

THE GREAT STEP

THE GALLERY TOP END SLOPE

yP(¦PetrieCR¦b58) = b/5 see GS algebraic arithmetics

CHEIOPS PYRAMID GALLERY SOUTH END

THE GREAT STEP — and its Gallery Top

WITH VALUES FROM FLINDERS PETRIE 1883

 

 

A full Petrie value corresponding rJCIRCLE calculated comparing description of The Cheops Pyramid Gallery

is given in these sections:

 

   CLARIFYING PETRIE POINTS ON THE GREAT STEP

 

   THE Abstruse Conic GALLERY HEIGHT

 

   PEARL LINE REFERENCE

 

 

 

PetrieCH7.36 gives no other information than this:

”.. and its lower edge is therefore at half the height of the gallery, that varying from

167 to 172.”:

167 + 172 = 399’’ — an averaged Petrie mean value for the Gallery vertical height with no further specifications.

   Wikipedia (The Great Pyramid) gives a value

8.6 M = 338.58’’. But its source is (here) unknown [See Miatello2010]. We have no further relatable references.

— Our Golden Section paragon body (although rough) gives [ProvDETill] a close (7.5pixel) value on the scale 4534.2’’/100pixels: 7.5(SCALE) =

340.065’’. PetrieCH7.46 In Quote Row1 neither gives guiding tolerances.

— But the rJCIRCLE complex gives more precise information, see links above — to be tested when and if more precise Cheops data appears.

 

 

 

yPGcalc: yPG

Petrie’s indirectly affirmed 1658.2 yPG value

— by trigonometric details in PINver1658:

 

 

——————————————————

TP27 ¦ PINver1658 ¦ PetriePG

 

 

 

yPGcalc¦rJ: FromB

OVERVIEW Cheops Pyramid after Flinders Petrie — SEE BEGINNING FROM THE CONSTRUCT FOUNDATION LINE

THE yPG GALLERY POINT CALCULATION

SEE ALSO COMPILED THE CONSTRUCTatB and THE TRANSPOSITION and the KingEquivalents

 

 

The rJCIRCLE complex calculated Gallery pG¦PG point connects GcoW2 to the Petrie central northern Pyramid entrance’s Cheops Pyramid 19th masonry course. That is In Quote PetrieCH6.31 Row4  from where Petrie deduced his (TCA) method with some help from ”the other Pyramids” to settle and measure the entrance parameters. The inner design measures and quantities all depart from and connect to that onset, as also here is accounted for.

 

—————————————————

rJCR¦b16 ¦ xyB ¦ yBarm ¦ B point ¦ PetrieIndirectlyVerified1658 — how the rJ calculation defines Petrie’s measures

 

 

THE Cheops Pyramid Inner Design CONSTRUCT IN SHORT:

— The GS-body ArcTan˝-line defines a set of 7 fundamental points (TCFL). From complementary additional GS-positions, intersection coordinated results define all further quantities. The 1883 Flinders Petrie measures are the finders guide.

 

GalCalcOW — 1: GCOW2

GALLERY CALCULATIONS OVERVIEW part 1

The Gallery PG(pG) point is calculated from The B point through the two GS-body

Pyramid Agents rJCR¦b16 and PetrieCR¦b58.

 

All quantities in this presentation have been deduced in guidance under the 1883 Flinders Petrie measured Cheops Pyramid values from the rJCIRCLE complex.

 

The yPG point quantity

appears from ENTER the GS-body primary PHASE 1 Result Table determination of the different basic points on the ArcTan˝ line at point B.

 

B-point illustrated

The descending entrance tunnel floor B-point is calculated from  the UPPER-GS position (B upper roof) and its intersection with the given basic ArcTan˝ line. The corresponding B-Lower point results from the corresponding LOWER-GS position (B lower floor). The vertical difference between these through the primary B-point defines the yATH- parameter — with further.

   All these values are calculated from the agent rJCR¦b16.

   Additional values from the agent PetrieCR¦b58 is then utilized with the b16 agent to generate fix constants between the two bOFFSET slightly different agencies: We take advantage of the difference between their horizontal coordinates which gives us a set of basic constants:

 

  yBarm = yATH  +  BUARM ¦

  yBlimit = yConB + yConBoffset = yConHBALimit = yConB + SIO

  yConOFFSET ¦ yConBUARM ¦

 

With these fixed exact calculated GS-constants we arrive — at first — at a practically direct vertical hit (1658.17’’) on the corresponding Gallery south sloping top floor point yPG within the Petrie given tolerances (1658.2’’ ± 0.2).

   At second (and third): these constants also connect to the entrance constructive quantities and their Petrie mentioned importance at the 19th course, see In Quote PetrieCH6.32 Row11.

 

TGS1:

The Great Step — detailed: The MiUNIT 61.80’’ = 100R

 

Petrie100RSource;

PetrieCH7 mentions the 61.7 value (± 0.8 or ± 0.9) 5 times:

 

 

With a broad given Petrie tolerance ± 0.8’’ we easily identify a specific Golden Section Cheops-MiUNIT:

S = 100R = 61.8033988..’’ rounded 61.80’’.

 

The reason GalleryTop for our illumination of the S=100R=61.80’’ unit here is simple

 

+ [(PetrieCR¦b58 = 4534.20’’)/√5 = 2027.76’’ = yP]

[(S=100R=61.80)/2 = 30.90]

[GalleryHeight = 338.76’’]

= 1658.2’’ = yPG as calculated from rJCR¦b16

 

 

Collected Petrie data on TGS: CLARIFYING PETRIE POINTS

 

 

The south end Gallery ramp Step Face with its top floor King’s Chamber level south following S=100R-value

marks the transition from north to south

— »EXACTLY» in the pyramid’s midpoint vertical as described by Petrie In PetrieCH7.46 Quote Row30 Pyramid Mid.

— See The yPG Calculations.

 

 

26° 12’ 50’’     PetrieCH7.39 In Quote Row34, ”mean angle of both passage and gallery together”.

CU        Adopted CheopsUNIT 100R = 61.80’’. See Petrie’s 5 quoting places of 61.7 ± .8.

CT        PetrieCH7.46 In Quote Col1 Row22 partly differently East side diverging value at site.

ΔMID   PetrieCH7.46 In Quote Row30 ”.4 ± .8  S. of the Pyramid centre”.

34.88 ¦ 4.16     PetrieCH7.46 In Quote Col1 Row37; ”34.88 — .64 — 30.08 = 4.16”, ”say ± .2”.

30.08   61.1 · Tan(26° 12’ 50’’) = 30.083332661, PetrieCH7.46 In Quote Col1 Row37.

34.88   measured (mean) step face height in In PetrieCH7.46 Quote Col1 Row34.

Petrie’s given tolerance ±0.2 with 34.88 allows max 35.08: we are allowed to adopt a 35.013 as below.

yV              1689.0   Petrie’s (measured/calculated) virtual sloping floor end at S. wall.

yK               1693.2   1689 + 4.16 = 1693.16 → 1693.2 ”± .6” In PetrieCH7.46 Quote Col1 Row42.

35.0       Adopted mean from PetrieCH7.46 In Quote Col1 Row18; rJequiv. 50R + yBlimit = 35.01295616 rounded 35.013.

 

 

 

 

PHASE1: —  The 7 Points Construct Foundation Line ¦ Jan2020 ¦ PHASE2 ¦ ENTER ¦

 

 

SEE SHORT INTRODUCTION IN NatCH

PHASE 1

Quantitative Determination of The Basic Properties

 THE FOUNDATION LINE CONSTRUCT

The CONSTRUCT FOUNDATION LINE

  THE 7 FOUNDATION POINTS — K L M G H B A

 

 

 

TABLE OF RESULTS Jan2020: — THE 7 FOUNDATION POINTS — K L M G H B A

 

This table of resulting quantities define all the points lying on The ArcTan˝ line in its intersection with the ArcCot √R line — the actual Cheops Rectangle ideal casing surface slope C° = 51.82 72 92 38 = 51° 49’ 38.25’’ from the Golden Section paragon geometry.

 

 

BASED ON A PRECISION OPTICAL QUANTITY MEASURE by Flinders Petrie in (publ.) 1883

we use the mathematically well defined GOLDEN SECTION GS-body paragon as below. Its unique mathematical pyramid (here coined »Cheops Rectangle») bd=h˛ geometry views a corresponding IDEAL Petrie Cheops Rectangle Petrie¦CR from Petrie’s measures on Cheops Pyramid, the Petrie¦CP.

 

Differences outside illustration — see illustration in ScaleDiff

— In this scale, even with the pyramid form (height or base) covering a total computer screen of 12 inches (0.3M) differences between Petrie¦CP and Petrie¦CR or even rJ¦CR will not appear to our optical eye due to the (very) tight small physical differences at the actual building.

 

GSParagonArithmetics: GS body Paragon

 

The inner pyramid design in this illustration has been as thoroughly as possible adopted to the measuring values from The 1883 Flinders Petrie measurements.

The lower shaft or well (next to x) has not been drawn out here as Petrie [”so evidently utilitarian”, PetrieCH7.46e] never made measures, while other authors (HelpILL) have made slight different approaches: no related data on this part is yet known except for the end openings. The marked red point is where we onset a pair of compasses to envelope the rectangle [bd=h˛] defining the Golden Section Relation number R = [√5 — 1]/2 = 0.618033988, with (many) equivalents.

 

 

Deductions to all mathematical expressions and connections used here of our gauging GS-body are (also) shown in more detail in (Swedish edition from Nov2017) GS-GEOMETRY with all the basic MATHEMATICAL CONNECTIONS.

 

GSTarCO: The7

 The Golden Section paragon geometrical quantities — exactly DEFINING THE 7 FOUNDATIONAL POINTS

 THE FOUNDATION LINE CONSTRUCT

The CONSTRUCT FOUNDATION LINE

  THE 7 FOUNDATION POINTS — K L M G H B A

The 7 GS-body xyCoordinate points [TarCO] ¦ The AG-condition ¦ ConENTER ¦  Petries19th ¦ The dSIDE ¦ ConPENT ¦ The P-point ¦ The B-point  ¦

 

Based on Table of results

OUR exercising MISSION:

Our exercising mission is simple:

— Use the given GS-body — as illustrated in the Table above — to extract the most simple and direct VISUALLY seemingly FIT with the given (Petrie) measured edifice.

 

 

 

The xy-origo is related to the pyramid’s north side base point, rightmost in this illustration.

+xy rightUp, —xy leftDown.

 

Below is the account for all the readouts of all the xy¦P-coordinates for all the Table parts K L M + G H B on the central ArcTan˝ sloping line. It ends on the point A-intersection at the pyramid ideal casing mantle side by the GS-body angle C° = ArcCot √R.

— The aim of this ArcTan˝ line specific exercise is to ASSERT and CERTIFY any person that the given KLMGHB-points define one and the same, and only so, ArcTan˝-slope ON the A-intersecting point, giving one and the same, and only so, end point intersecting xy-values:

— We must be VERY sure on this point, so no hazard or adventure will pop up later. Because this IS the foundation of the whole quantitative concept, as will be seen.

— The Table shows the results as a perfect certification on all the named points:

The ArcTan˝ line point coordinates: ArcTan˝ Line ¦ GSTarCO

We relate the Tabled-used GS-geometrical KLMGHB-xy coordinate points here from the given GS-paragon’s visual fit (some acquaintance is needed to familiarize the connecting GS-geometrical details: without further, we assume full insight):

 

Kx         —b(1 + R^3 + R/√5) = —b(1 + b4 + PiLINEx)

Ky         b(1//√5 — 1) = P — b

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

Ly         b(1//√5 — 1/2) = P — b/2

Mx        —b(R/√5 — 0.4R^3) = —(PiLINEx — 0.4b5)

My        b(1/√5 — R^3 — 0.8R^4) = P — (b4 + 2 · 0.4b5)

   CLARIFYING xy¦M:

— The often useful hABb  triangular formula can be utilized to find the form of xy¦M:

 

hABb triangular formula 

 

— There is another perpendicular ArcTan˝-line with the same internal (in a lower GS-fraction) GS-property as our main ArcTan˝-line. These two intersect in the point Pb where the xM-part is calculated directly as illustrated:

b5REF: GSTarCO

 

The triangle ArcTan˝-90°-ArcCot˝ gives for two consecutive calculations from hypotenuse (b) to longest right-angled side (b/√1.25)/√1.25 = b·0.8;

— As always sin˛+cos˛=1, the corresponding end shortest side will count by b·0.2

— for the ArcTan˝-triangle only.

 

PiLINEx — 0.4·b5, see illustration above through the hABBb connection.

— Given Mx, also the vertical My-part becomes directly given as twice the Mx-part through ArcTan˝:

2 · 0.4b5 = 0.8b5 = My-part.

 

Gxy:

 

The xy-origo is related to the pyramid’s north side base point, rightmost in this illustration.

+xy rightUp, —xy leftDown.

 

 

Gx        —b[1 + R/√5 + R^3 — 2(1 — 1/√2)] = —(PiLINEx +b4 — 2|Gy|) .......        = -4221.8156658449’’¦4221.82

PETRIExP = xG + 10R ..................   = 4227.9960057324’’ ¦ 4228.00

Gy         —b(1/√2 — 1/√5) = —(b/√2 — P) ..............................................................  = -1184.0412529906’’¦1184.04

PETRIEyP = yG — nValue ..............    = 1181.2240228242’’ ¦ 1181.22 NOMINAL

PETRIEyP = yG — nValue ..............    = 1181.2313270982’’ ¦ 1181.23 piVERSION

   CLARIFYING xy¦G:

— The GS-body is explicitly clear on this point:

— The GS b-diagonal intersects the b-square’s partial GS-circle in the F-point through the inverted 2-root:

y-part = b — b/√2. Related to the the upper we get a simple total  My = —(1/√2 — P).

x-part = twice the y-part through our ArcTan˝ line: x/y=2. Mx in total then: b—2My+b4+PiLINEx, or

minus(PiLINEx +b4 — 2|Gy|).

Hx        = Ax ............     Hx can only be calculated with respect to a given ArcTan˝ endpoint.

Hy         0 .................     H intersects the Petrie pavement measuring ground reference line.

Bx         see PHASE 2.

By         see PHASE 2.

Ax         same x-intersecting result from all four KLMG-points

Ay         same y-intersecting result from all four KLMG-points

 

Phase1RESULT: PHASE 1

SUMMING RESULT — The Construct Foundation Line from Pyramid North:

All KLM GB share exactly the same ArcTan˝ line with one and the same end point

xyA -523.0566039073’’;665.3382779782’’ on the pyramid ArcTan R-side.

— These basic reference points define the further inner design points of the building.

OverviewRESULT:

Rough Overviewing RESULT

 

PHASE 1:

— The G-point and the A-point explain the absolute basic quantitative inner Cheops Pyramid GS-design;

— THE FOUNDATION LINE with respect to the crucial G-point as illustrated below in a compressed overview. This illustrative approach is greatly exaggerated from the actual view by purpose of enhancing and elucidating the else-way tight differences between the several slight differing angles and values. We will relate these in detail.

SCHEMATIC OVERVIEW — Cheops Pyramid inner design:

 

 

See also fully related the corresponding/equally Petrie calculated angular values in TP27.

See also The Petrie D point.

 

(PG→yBlow)°     ArcTan˝ ........   rJCR¦b16

(pG→yB)°          26° 1’ 3’’ ........   rJCR¦b16, PetrieCR¦b58

(pG→B’)°           26° 12’ 51’’ ....   PetrieCP

(D→B’)°            26° 3’ 59’’ ......   PetrieCP

(D→pG)°           26° 12’ 34’’ ....   PetrieCP

————————————————

Because the Petrie measures NOW are PRACTICALLY defined by the two pyramid agents rJCR¦b16 and the ideal corresponding Cheops Pyramid as the Cheops Rectangle PetrieCR¦b58 — their difference is discernible — it makes no longer a difference if we calculate directly from the Petrie given measures — including his given tolerances — OR if we calculate directly from the actual pyramid agents and their exact zero tolerance: all values become collected anyway within the the Petrie given tolerances.

 

ROOF18: Proving the 19th

Further ahead

A SECOND A-POINT DECISIVE QUANTITY RESULTS FROM THE FIRST A-POINT RESULT

The Petrie 19th course — Petries19th — floor construction level

 

 

 

 

yA + n = Petrie’s18th roof. Case Closed.

 

There is no any the slightest doubt that the 1883 Flinders Petri working group measured Cheops Pyramid has definite quantitative constructive properties connected to the rJCIRCLE and its ideal Cheops Rectangle geometrical (nuclear) mathematical physics.

— IF we would be the ones who should build a monument for a future humanity to find proof on fundamental nature harmonic nuclear grounds, this would definitely be it.

 

With a Petrie given (broad)) tolerance ± 0.1’’ (± 2.54 mM) on the 19th course floor height over the pavement, the rJCIRCLE calculated quantities 668.15’’ or 668.16’’, depending on convenience, can be apprehended as a direct constructive hit. The difference from the nominal 668.2 is only 0.05 or 0.04. That is only 1 mM — still after (many) thousands of years.

 

 

See first, unless already acquainted,

The AG-condition

Why there is only one unique parallel relationship rJCR¦PetrieCR.

Then the actual connecting explaining in

ConENTER

How the A-point Defines THE DECISIVE Petrie 19th COURSE floor level  by the established 7 points AG relations (TarCO)

Then the additional (very) interesting

ConPENT

How Petrie Reckoned the Cheops Pyramid Entrance.

 

 

PHASE 2:

— The B-point explains the inner design ”final count down” with respect to the so called Great Gallery and its dimensional and angular properties.

— Point B positions the point where — by ideal construction and a corresponding (later) measure — the downward and the upward tunnels meet, and how the construct point matches the Petrie measuring values.

 

As instructed by Petrie’s given measuring tolerances, NO QUANTITATIVE DEVIATIONS will be accepted here. This expedition is solely dedicated a fundamentally tight an maximum exact examination of the agreements, coherences and concordances between Petrie’s values and those emanating from the rJCIRCLE complex: The Cheops Rectangle’s ideal Golden Section paragon math. Our two EXACT GeoMATHematical agents rJCR¦b16 and its ideal spouse Cheops Rectangle PetrieCR¦b58 determine the resulting quantities: The one and only unique bh=h˛ Cheops Rectangle pyramid construct.

 

Phase1RESULTpointG:

SHORT OVERVIEW

Phase1RESULTpoint ¦ G

 

Some complementary rJCR¦b16 calculated results are shown in the point G region below.

— See the rJCR¦MEAN 45.93’’ math in DescendingPassageLowHigh.

   Two different GS-body projections form a mean construction line between two Petrie given values.

 

 

The plain text values are:

PetrieCP¦b         4534.40’’± 0.25

PetrieCP¦x          ”4228 ± 2 ?”, PetrieCH7.36e¦64tab

PetrieCP¦y          ”1181 ± 1 ?”, PetrieCH7.36e¦64tab

PetrieCP¦height  ”48.5”, PetrieCH7.37e, [”as deduced from the roof, which is better preserved”]

PetrieCP¦height  ”38.3”, PetrieCH7.37e, [  ].

—————————————————————————————

rJCR¦b16         4555.88 .......  the actual exact rJCIRCLE Cheops Rectangle pyramid half base

rJCR¦b58         4534.20 .......  rounded to two decimals from b = 58R√16000 = 4534.1965576 ¦ featuring an ideal PetrieCR

 

 

The GS-quantities here are taken from the xyG column in Phase1TABLE OF RESULTS.

More precise and detailed G region quantity representations are given in Main Construct.

 

 

 

 

ConAG: HowSTART ¦ Phase1

THE AG-CONDITION

WHY THERE IS ONLY ONE UNIQUE PARALLEL relationship

BETWEEN THE TWO IDEAL GEOMETRICAL CHEOPS PYRAMID AGENTS

 

 

The values below comes from The Result Table.

— Because the two geometrically ideal exact but differently sized pyramids rJCR¦b16 and the ideal PetrieCR¦b58 have only one unique mutual projective distance through parallel straight lines, other coordinate relations between the two will have other (unique) parallel relationships.

 

 

 

 

 

 

Prioritizing the G-point determination from a relation based on the pyramid ideal (A) casing flat surface, will establish a fixed and definite, non changeable relationship between these two basic outlets — hence determining an entire constructive — exact quantitative — layout of the whole building.

 

The vertical (y) offset difference — yConOFFSET — between the two is

 

yConOFFSET = 4.4106512044’’;

— See NatCHintro for the iconic details, unless already familiar.

MOST SIMPLY CALCULATED AS ABOVE the yConOFFSET quantity is found

through the ArcTan˝ triangle, in absolute values:

(yA — yA’) + (xA — xA’)/2 = 4.4106512044’’:

 

 

Because this offset is related to BOTH pyramid agents ON THE SAME LEVEL

— the main rJCR¦b16=4555.88’’ and the actual Cheops Pyramid’s corresponding physically ideal Cheops Rectangle PetrieCR¦b58=4534.20, as within the PetrieCP¦b=4534.40 ± 0.25 tolerance

— its RELATION is also conserved as such:

— a TRUE Pyramid Constructor Base Line is established.

   The offset value can be — and is — used in defining possible exact connections to the Petrie measured Cheops Pyramid values — or not at all.

 

For the G-point determination coordinates, see TarCO from PHASE 1.

 

 

 

ConENTER: 18Jan2020 — PHASE1Confirming 19th ¦ The Petrie Point ¦ Pangle ¦ Hangle ¦

 

 

The GS-body Paragon Pyramid

CONSTRUCTION Entrance Point (A)

After having noted THE FOUNDATION LINE CONSTRUCT — a complete match from Petrie’s measurements of the Cheops Pyramid along with an explaining geometry — it will HERE be more convenient to take this lead:

— EXPLAINING THE CONSTRUCTION. Along with presenting the quantitative matches.

— And of course: yearning for any opportunity to meet with a general failure.

 

 

CARING TO TO PRESERVE THE CONSTRUCTION LINES

some offset to the actual physical floor must be granted.

   Taking the basic Cheops Rectangle unique bd=h˛ Pyramid coordinates from the GS-body with our two agents

rJCR¦b16 and PetrieCR¦b58

we arrive at the following basic picture:

ENTER: MainConstruct 

RelatedPetrieSPOT

Enter

665.34 + 2.817 = 668.157 ~ 668.16’’: Petrie’s 19th course floor ”668.2 ± 0.1”: ............    clearly approved  ...........     the exact original

665.3382779782 + 2.8172301665 = 668.1555081446 = yA + nVALUE¦norm

665.34 + 2.810 = 668.150 ~ 668.15’’: Petrie’s 19th course floor ”668.2 ± 0.1”: ............    clearly approved  ...........     the pi-number adopted version

665.3382779782 + 2.8099258924 = 668.1482038706  = yA + nVALUE¦piForm

— Both these apply well within the Petrie given tolerances: 668.20’’ ± 0,10.

 

Pushing the far ends more close along the PARALLEL CONSTRUCTION LINES, see The AG- CONDITION,

magnifies the narrow angles — creating an exaggerated illustrative effect.

See also detailed math in Hangle [The H°Angle] and Pangle [The P°Angle].

 

The GS-paragon Pyramid Entrance: ENTER

 

 

See also yConBoffset and [18thRoof] PROVING THE PETRIE 19th Floor — 18th Roof — ARITHMETICS. The figures here — 1.4086¦2.817¦3.1497.. — reflect the exact PetrieCR¦b58 and rJCR¦b16-calculated original through the points AA’ GG’. In examining these values, the number of pi = 3.1415926.. has been adopted as a slightly more favourable — yet close — value for the ease of reference. The difference between them is anyway insignificant with respect to the Petrie given tolerances. By the same standard of our convenience, the quantity 10R has been adopted — as it is practically the actual Petrie horizontal offset relative the rJ G-point. It is here assumed, that these convenient figures also would have attracted the original constructors in giving us, here in our aftermath, a not to difficult way of »cutting to the chase».

Note that Petrie [See full Quote in PetrieCH6.24] measured the [idea of the original] casing pyramid from the remaining staircase masonry slope values, and a few of the casing stones at the base.

— In this illustration on the scale of single inches, the differences are factual and directly inspectable.

— The CASING blue line represents the Petrie staircase measured slope 51° 53’ 28.6’’ while the orange part belongs to the ideal GS-body

Cheops Rectangle ArcTan 1/√R-value 51° 49’ 38.25’’.

 

SpotLimit: ENTER

yPonB: yConB ¦ SIO ¦ yBlimit

 

yPonB = 18·TanPangle — 2·yBlimit = 0.7603999237’’.

yPonB directly appears from the Petrie B point definition as an overlayed extra vertical offset factor »y UPON b».

yPonB connects the actual physical floor, its possible sight line, with the pyramid’s outermost visible material — as seen from inside the narrow 105 M long dark descending tunnel .

— With its quantity we can calculate the exact optical window through the descending tunnel for Petrie to spot the casing region from where the 19th floor properties were derived.

   See further full details from ENTER, The F Angle and Proving The 19th Floor Arithmetics.

 

GSbasic: ConEnter

Taking The Basic.

 

 

This presentation shows

   how the parts of the building are tied together by exact quantities between an original rJCR¦b16 and PetrieCR¦b58 casing and the GS-body’s advised parts and their constructive layouts.

   The Topics below link to actual sections.

 

Confirming The 19th ¦ The Petrie Point — overview ¦ Main Construct ¦ Floor Construction Angle ¦ The Petrie Point ¦ Petrie Ref. H-angle

¦ H-ANGLE CALCULATION ¦ Confirming The 19th ¦ ResultsBasic ¦ 

— See full quote of Petrie’s 19th floor in Petrie’s19th.

 

   a confirmation of the whole inner design of the Cheops Pyramid through exact numerical quantitative values with zero tolerance connecting to the GS-paragon body — depending entirely 100% on Petrie’s onset on the entrance complex. See from ENTER.

 

Specific rJCR¦b16 A-G values are taken here from The Result Table — both pyramid agents A-G values are as calculated from the CalCard:

 

 

 

The Result Table text section details how the coordinates were calculated from the GS-body paragon geometry.

 

The Petrie Point: ThePePo

OVERVIEW

The Petrie P point

 

The bottom  GG’ points from the two exact GS-body agents rJCR¦b16 and PetrieCR¦b58 form a

2n BAND MARGIN with nominal height  5.63’’.

— In the middle of the GG’ 5.63 height stripe we find the corresponding Petrie point P value slightly (+0.225’’) positioned over the GG’- midpoint.

 

With the PetrieCH7.36e given height

1181’’ and Petrie’s given tolerance ”± 1?”, we see that the difference 0.225’’ is negligible

— like »a perfect hit».

   We can’t prove it is NOT. And we can’t prove it IS — except the fact that it is positioned within ”it is”: approved with tolerance. So »it is».

— The constructive ideal midpoint in P’ (P prim) is calculated from the rJCR master G -point through an end edificial condition:

 

MainConstruct: COMPRESSED VIEW —  ENTER ¦ ConENTER ¦ EnterGSPyramid ¦ ThePetriePoint ¦ Pangle ¦ Hangle

— G’ values [GENERAL PRIM-] use the PetrieCR¦b58 = 4534.20’’ agent and the G-values use the rJCR¦b16 = 4555.88’’ agent. See CalCARDmethod.

Given the PetrieCH7.36e¦64tab Petrie xy P measured values 1181; 4228 and their relatively hight xy tolerances,

as quoted ±1?;±2?, and our two above named pyramid agents calculated yP’ value

1184.04 — ([1184.04 — 1178.41 = 5.63]/2 = 2.815 = n) = 1181.225’’ or more precisely without decimal cuts

1184.0412529906 — 5.6344603329/2 =

yG — n        = 1181.2240228242 with a nominal Petrie difference 0.2240228242, 2 decimal rounded as 0.224’’

PetrieyP      = 1181.0 ± 1 ?

showing only a nominal Petrie measured vertical difference of 0.22’’

there is no scientific way for us to exclude a compelling fact that we are looking at a highly intended construct PLAN. The more so in observing the close and convenient horizontal PP’ difference between our calculated 2 decimal rounded 4221.82’’ and Petrie’s nominal 4228’’ as exactly 61.8’’ = 10R:

xG + 10R     = 4227.9960057324

PetriexP      = 4228.0 ± 2?

 Compare ROSSI2002: As we know it [with some reservations], the 2 500 BC Egyptians hardly even knew anything at all about 2R = 5^˝ — 1; R = 0.618033988.

— And MiUNIT: it had to be in INCHES too. So: Classic Modern Academic ancient Egypt scholars seem not to have much mandate here: A past GeoATLANTIS is calling attention.

PetrieCP¦xP .................  ”4228 ± 2 ?”, PetrieCH7.36e¦64tab

PetrieCP¦yP..................  ”1181 ± 1 ?”, PetrieCH7.36e¦64tab

 

The nValue:

SECURING THE BASIC GS-PARAGON CONSTRUCTION LINE AG from hazard — burying it in the bulk masonry, yet preserving its geometrical foundation — demands some definite offset to an actual corridor floor (the Petrie named Descending Passage tunnel from the pyramid north casing side entrance A).

— A maximum G-point right angled GP’ offset can be calculated BY USING ONLY NATURAL (mathematical geometrical [transcendental — any SAFELY KNOWN available, easy to deduce]) CONSTANTS by intersecting the GG’ mid-line with an AG-normal (|_) from point G as follows:

 

The P°Angle: MainConstruct ¦

— With a more direct decimal calculation: GG’ = 2n = 5.6344603329; n = 2.8172301665

(GG’/2 = 2.8172301665) × √1.25 = 3.1497590802’’ ¦ (pi = 3.1415926)/√1.25 = 2,809925892 = MODIFIEDnValuePiVersion;

n = nValue = pi/√1.25 = 2.8099258924’’ ¦ pi [π] = 3.1415926;

Pangle via piVERSION for nValue ........ 2.8099258924: ...........  26° 31’ 17.48 60 86’’;

Difference to Petrie’s PangleLow 26° 31’ 18’’: ........................................ 0.51 31 40’’.

Pangle via GG´/2 for nValue ................  2.8172301665: ...........  26° 31’ 17.07 87 56’’;

Difference to Petrie’s PangleLow 26° 31’ 18’’: ........................................ 0.92 12 44’’.

WITH SOME ASSISTED CERTIFIED HELP FROM PETRIE’S GIVEN QUESTION MARK;

— We adopt IN TESTING THE CHEOPS PYRAMID SUGGESTED ADVANCED HIGH TECH PLANNING

the higher [possibly rounded as 18’’] as The Constructive the rJCR¦PetrieCR calculated P° angular value.

— But we will frequenly refere borth candidates to show that their difference plays no significant role on the overall constructive picture.

 

Petrie’s Pangle:

PetrieCH7.36e describes the whole tunnel’s mean angular value — see also in InvEX1:

 

” 36. [p. 58] The azimuth and straightness of the passage were carefully measured. The azimuth down the built part was taken by reference to the triangulation, which in its turn was fixed by six observations of Polaris at elongation, from a favourable station (G). The azimuth to the bottom of the rock-cut passage was observed independently, by five observations of Polaris at elongation. The observations of the straightness throughout gives a check by combining these two methods, and they are thus found to agree within 19”, or just the sum of their probable errors, equal to only .09 inch lineally on the azimuth of the built part.

 

The results are:

                                                    Azimuth             Altitude

Mean axis of whole length.         – 3’ 44” ± 10”                 26° 31’ 23” ± 5” ?

”.

FloorConstructionAngle: The P°Angle

Temptingly close to the conveniently inviting transcendental pi number 3.1415926, if we »buckle up and pine in» to that attempt as Presumed Constructors for aftermath students, we arrive at the destination

The Pangle

— The Construction Angle P° = AGP’

rJCR¦b16GAslope = 4135.338346’’ = (xG—xA)(1.25)^˝ = [4221.8156658449’’ — 523.0566039073’’ = 3698.7590619376’’]√1.25

P° = ArcTan˝ – ArcTan(π/4135.338346’’) = 26° 31’ 17.48’’

PetrieCP¦xP        ”4228 ± 2 ?”, PetrieCH7.36e¦64tab

PetrieCP¦yP        ”1181 ± 1 ?”, PetrieCH7.36e¦64tab

See also this Petrie angle in Investigating Example 1.

See also how the Pyramid casing entrance point A connects Petrie’s observations in EnterGSPyramid.

The Petrie Point: ForCA 

 

10R — The Petrie P point (P)

 

— Obviously on »a float of Natural Constants», we might as well »throw in» an extra additional 10R (MiUNIT/10) »to get some distance to the Petrie xP-point» and its x-value:

 

rJ-DEFINITION OF THE PETRIE P POINT

rJ-DEFINITION OF THE PETRIE Subterranean P POINT

 

In

PetrieCH7.36e¦64tab

”4228 ± 2?”

compared to the rJCR¦b16 xG value

4221.82’’ ± 0.00 , we have

xP — xG = 4228.0 — 4221.82 = 6.18’’ = 10R.

 

(”And the hits just keep coming”).

   Exactly.

— That would be: a PLAN.

 

SUMMING UP

The Flinders Petri working group (1881-1883) obviously made excellent measures.

 

HangleIntro:

The Breaking point

(H, pyramid base cuts the ground level)

to the Casing Construct Original Entrance point (A)

The Central Aspect

 

— How about the (ForCA) illustrated BREAKING point at H, directing the floor to the construct original casing entering point A into the actual GS-body paragon, the Petrie named descending tunnel from the casing surface?

 

See HOW PETRIE RECKONED THE ENTRANCE for the math-part — and EnterGSPyramid.

— Petrie’s measuring arrangements (StationMark) explain the details in quote PetrieCH6.31.

 

 

The Crucial ¦ Petrie Hangle

See also: DRAWING SPECIFICATIONS in The Entrance.

 

 

The H°Angle: The P°Angle ¦ ThePePo ¦ Main Construct

 

The H° angle — The Hangle

PetrieCH6.32e: 26° 29’ ± 1’:

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

 

H-ANGLE CALCULATION: Hangle ¦ Pangle

 

As we know:

— There is only one referencing

Cheops Pyramid Inner Design Descending Entrance Tunnel CHEOPS RECTANGLE

region to which we can relate a Petrie corresponding angular value of 26° 29’:

— Where the  IDEAL CHEOPS RECTAngle Pyramid base intersects the ground zero level:

— The H-point connecting the fundamental (Enter)casing A point.

 

 

 

See Finding d.

 

 

SOLUTION (with an investigating lead as Testing Constructors):

— We simply and undramatically BORROW the calculated dValue from the primary defined subterranean part (Petrie P ¦ Enter) and HANG it as a right angle distance onto the given ArcTan˝ foundation:

— This will NOT result in any construction part. It is ONLY a METHOD for us — the only SIMPLE deductive one we know of here — to acquire a 29° 21’ angular value from the given Most Simple premises. Then we can use this with parallel constructive levels to settle a final actual physical construct (whatever seems suitable for the purpose).

 

 

 

Simply as illustrated:

H° angle = Hangle = ArcTan˝ — ArcTan(d/2yA√1.25) =

Hangle = 26° 28’ 58.54 67 58’’

PetrieCH6.32e: 26° 29’ ± 1’:

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

— Approved.

   APPLICATION — nearest:

— See yConB: how the rJCIRCLE complex determines the decisive Petrie B point.

 

Confirming19th: FINDING THE d-SIDE ¦ HangleCalc ¦

Finding d (2.13’’) — with a confirmation of Petrie’s 19th floor

 

 

 

Selecting a lower P’G-value than the default — we adopt the pi-value 3.1415.. instead of the slightly longer default 3.1497.. — means we change the basic conditions: However, preserving the 10R = c as a constant separating distance, we adopt the other parts to it and finalizes by calculating d over the former (minimum) derived angle (P° = 26° 31’ 18’’ with the use of pi for P’G). The end results will show us anyway how this works — if at all. [It works].

 

 

RESULTING VALUES:

 

n1 = π/1.25                                ;

n0 = (yb16yb58)/2

c = (10R=6.18) – n1¦0/2               ; = 4.7753769413’’

e = c·Tan                                  ; = 2.3831554097’’

PREFIXxSIN [PREFIXxSIN] : d/e=sinP°; (d/c=cosP°; d=e·sinP°=c·cosP°);

d = sinP°                                   ; = 2.1323680500’’

H° = ArcTan˝ – ArcTan(d/L)     ; = 26° 28’ 58.5467583038’’

L = AH = 2y(A)1.25          ;

 

ResultsBasic: Confirming19th ¦

RESULTS:

26° 28’ 58.55’’ ..................  H angle = 26.4829296551°

PetrieCH6.32: ”(4) entrance passage angle at mouth 26° 29' ± 1'; ”

——————————————————————

Petrie’s Cheops Pyramid Course Floor No19 found

— defined and confirmed by rJCR¦b16 n+yA:

— Entrance (A) connects the 19th floor with subterranean (GG’) via

nValue + yA¦rJCR¦b16¦665.34’’ = 668.2’’:

 

d = 2.13’’:

P’G                                n                                    c                                    e                                    d                

3.1497590802          2.8172301665   4.7717248043         2.381321038            2.1307288152 26° 28’ 58.77’’

3.1415926536          2.8099258924   4.7753769413         2.3831554097         2.13236805 26° 28’ 58.55’’

 

 

Exact calculated values from the Golden Section paragon body NatCH through the rJCIRCLE¦b16 and PetrieCR¦b58 Cheops Pyramid Agents.

Compiled and presented 18Jan2020 for UNIVERSE HISTORY — no rights reserved: knowledge — universal energy — is for free.

 

 

 

THE H-ANGLE rounded 26° 28’ 59’’ ~ 26° 29’

— based on the d-side (also defining the P-angle minimum 26° 31’ 18’’)

— is just only practically 1 arc second (1’’) from Petrie’s 26° 29’ 0.00’’.

— With Petrie’s stated ± 1 arc minute tolerance our arc second difference has no meaning here.

   See also the Rossi2012 reference:

— The ancient Egyptians (hardly, as we see it) knew The Math — as we know it.

   We are obviously dealing with a sophisticated and advanced mathematical and physical plan for the whole edifice.

 

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 ArcTan˝ 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 =       ArcTan˝         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 =       ArcTan˝         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 47.26In 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 1ORIENTATION

 

 

 

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 ArcTan˝ = 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: