CHEOPS ATLAS ¦
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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
Background.
The naming or THE TERM CHEOPS
RECTANGLE is my own early label: Tracking the original math connection bd=h^{2}
back to The Cheops Pyramid was clarified during a shorter library literature
research (See sw. HistoryBackground [around the
time when Intel presented its first microprocessor 8080]).
The term CHEOPS
RECTANGLE was adopted by this author after a late
20th century detective search in libraries: The most early known mentioning
of the unique and very geometrical-developing useful connection bd=h². It was
rhetorically used by Galileo Galilei, Apollonios and Pythagoras, further
backwards mentioned as an Egyptian ancient form connected to the Cheops
Pyramid.
We respect that tradition here,
and adopt the term to it.
k0 ¦ GOLDEN SECTION BODY R ¦ 18 ¦ rJ ¦ rJCR¦b16
ENTER MiUNIT. These and others provably breach
modern archaeological ideas of the origins: exact quantitative proofs. A
correspondingly exposed building plan appears: as so extracted from
the rJCIRCLE
complex:
GOLDEN SECTION CHEOPS RECTANGLE MATH.
We study the
details: THE TWO PYRAMID CONSTRUCTIVE
AGENTS.
CONTRACTED CONSTRUCT: Main OVERVIEW The
Cheops Pyramid proof of a Contracted Construct ¦
RECURRING CONSTANTS @3 SITES The cSIDE
The GOLDEN SECTION Cheops Rectangle Complex ON the actual physical Petrie 1833 measured CheopsPyramid
No
uninitiated will
understand |
||||||
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 Pyramids ½ square base (PetrieCP¦b=4534,40
± 0.25) can has shown to
be calculated with excellent precision. That we will expose in this
presentation on the shoulders of all those who have made contributions to the
Petrie established Cheops Pyramid metrics, their tolerances and presentations.
To be noted: Several later 20th centuries
sources have verified and asserted Flinders Petries 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
THE
INNER DESIGN OF THE PETRIE MEASURED CHEOPS PYRAMID IN rJ EQUIVALENTS
Beginning
(BackGround)
from the so called Queens Chamber:
QUEENs CHAMBER
See also part of the below in IntroEX R = [√5 1]/2 ¦ b1 = rJCR¦b16 = 4555.88:
rJCalc: A = 1790R hOFFSET ¦
B = A 97R ¦ C = b1/2√5 ¦ D = 1350R ¦ BD = 254R
+ hOFFSET ¦ AD = R[97+254] + hOFFSET ¦ EF = 333R ¦ FG
= ¦ b1/21 ¦ J = 1350R +
π·[5·18 + 16]/5 ¦ H = J 75R ¦
»The Egyptian working crew must
have been psychic». MustBuyBook.
Scuse me: Several Tight Nominal fits around 0.005
inches is definitely no coincidence.
QUEENs 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
5GoldenSection ¦ 18CheopsRectangleNuclearConnector ¦ 16PyramidAgentNumber ¦ π ¦ R ¦ type R(n+18^{2})
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 Χ (PetrieCR¦b58=4534.20 OR
PetrieCP¦4534.40) · R^17 = (2.53945.. OR 2.53956.. ) ~ 2.54.
Both apply.
KINGs 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:
KINGs 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:
Petries 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 Petries 14.5, summed up
with 47.4 gives exactly 61.8 = 100R.
The
Petrie mentioned 7 LAPS from Gallery roof top down to the Pyramid S. wall then
evenly counts as
14.4 = 7 · 1000/(3 · 9 · 18 + 1/9) = 7000/(486 +
1/9) ¦ 14.4 + 47.4 = 61.80;
14.5 with modified 47.3 gives the same
Cheops MiUNIT 61.8 with an even 7 resolution
14.5 = 58/4 = 7 · (2 + 1/14) ¦ 14.5 + 47.3 = 61.80;
The PetriePLATE.9 drawing in comparison (above right: magnified from the @Internet
Source original) shows a fair
resemblance. But no further related data on this part is known here.
See further on THE GALLERY
POINT ¦ THE
GALLERY TOP.
CheopsATLASintro: MP1: Compiled 19Feb2020 ¦ PART 2 ¦ PART0
CHEOPS
PYRAMID CONSTRUCTION PLAN DETAILS SETTLED by rJCIRCLE Complex Jan2020
FULLY PETRIE CERTIFIED CALCULATED QUANTITIES
Constructive OVERVIEW WITH LINKS by order of deduction PART
I ¦ all Pyramid measures in Inches: 1INCH = 0.0254 M.
AT FIRST TO BE OBSERVED WITH 100% CLARITY UNLESS ALREADY
FAMILIAR: The NUMBER 18. We are dealing with a
connection of which modern academy scholars have no idea: TNED deducing not inventing nuclear physics through
natural constants The rJCIRCLE connection:
The Neutron Square atomic masses = experimentally
measured [HOP]
is completely unknown to modern academy. And it will never be adopted either:
modern academy ideas of nuclear physics IS a primitive Provable in every
atomic detail, or not at all. Faulty statements are not allowed here. This writ
focuses 100% on that statement.
ab:
With all the general data known of The Great Pyramid
CHEOPS PYRAMID from Flinders Petrie 1883, we see a beginning from the
absolute most simple (a: The GS-body):
The Most (a) obvious GS-body visual FIT generates (b) a foundational ArcTan½ construction line of 7
fundamental KLMGHBA xy COORDINATE points. 6 of them certifies the
genuineness of the 7th casing ENTER point (A) by intersection
math calculus by check and cross check reckoning. This is the foundational
construct line.
From the notified Cheops Pyramid
rJCIRCLE FIT, we use the two pyramid Golden Section agents (b1) rJCR¦b16 and (b2)
PetrieCR¦b58 as exact numerical agency quantitative generators to test their values
against the Petrie measured: they should DEFINE the Petrie working group
results within the Petrie given tolerances, or not at all.
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 (yGyG) of given
by the two pyramid agents within Petries given tolerances:
PetrieCH7.36e
states: ........ x4228±2?; y1181±1?.
rJcalc: ................................. x4227.9960057324; y1181.2240228242.
The ½(yGyG) nominal (2.8172301665) difference
(The nValue) has an ArcTan½ triangle
hypo-side (n√1.25=3.1497590802)
close to π=3.1415926.. Taking the suggestion, we adopt the piFORM as a
piVersion for n (and report occasionally throughout our results the
(discernible) difference between the two (asserting that any of them will do
..).
de:
Namely (d): Simply Summing yA + nValue directly defines the Petrie
measured 19thCourse Stone Masonry Floor Level above the Petrie pavement:
PetrieCH7.35 states
: ........ y668.2±0.1.
rJcalc: ................................. y668.1482038706. (ROUNDED
668.15→668.2). Nominal Difference: 0.052.
The details (e)
(ENTER) expose the connections.
fg:
The GS-body paragon gives us (f) direct interpreting instructions in how to connect the descending
and ascending tunnel parts through their common referring coordinate point (B):
At first the Petrie measured B-point is rJCIRCLE
complex
defined:
PetrieCH7.39¦64tab
states: x1517.8±0.3; y172.9±0.2.
rJcalc: ................................. x1517.7016293661; y172.9045085255.
NomDiff: x0.098; y0.0045.
The (f)
delicate Two pyramid agent Mutual Function Principle (TOMFIP)
actual physical pyramid and the ideal Cheops Rectangle rJCIRCLE
b16 agent
includes an internal bOFFSET value (21.68=21.6799079131). It obviously
functions as a »Construction Sealing Certificate» pushing the rJ-calculated
construction values into the final PetrieCR¦b58 agent featuring the real physical
PetrieCP measured edifice, as here described. So to speak:
No Cheops Pyramid Tourists are allowed to Understand
The Construct unless so »enlightened in the basics».
Most definitely no 1800+ modern academic scholars. Guaranteed excluded.
The B-point (f)
complex gives (g) all the summing constants and parts leading directly
to the GS-body Cheops Rectangle rJCIRCLE complex definition of the
height thickness of the PetrieCH6.32 unveiled and so decisive 19th course masonry
»pyramidic principle» (PROVING THE PETRIE 19TH FLOOR
ARITHMETICS):
PetrieCH6.32 states: .......... 37.94±0.17.
PetrieValuesCalc: ............... 37.9640590055.
rJcalc: ................................. 37.9657350065. DecDiff: 0.0017.
These coherences prove the affinity details between the
actual physical building and the Golden Section paragon
CHEOPS RECTANGLE structural plan.
CheopsATLASintro: MP2: Compiled 19Feb2020 ¦ PART1 ¦ PART0
CHEOPS
PYRAMID CONSTRUCTION PLAN DETAILS SETTLED by rJCIRCLE Complex
FULLY PETRIE CERTIFIED CALCULATED QUANTITIES
Constructive OVERVIEW WITH LINKS by order of deduction PART
II ¦ all Pyramid measures in Inches: 1 INCH = 0.0254 M.
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 Petries 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 Queens Chamber at the Gallerys 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 Queens 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:
Kings 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 Kings and
Queens Chambers in Multiple R Values.
KINGs 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 Petries 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;
The final collapse is approaching the condition of the
building around 1883, Kings 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 smallonly a matter of an inch or twobut 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 Kings 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 Petries 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+18^{2}) = 206.4233522425.
The corresponding Kings 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 Queens Chamber:
In the Queens 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+18^{2}) = 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.
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:
(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 dont 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.
QUEEN SPECIAL
Specifically for the QUEEN FLOOR LEVEL yQUEEN
contra the KING FLOOR LEVEL yKING, and the rJCIRCLE
complex
transition parts already used (even closer that the yQUEEN multi R-alternative):
THE QUEEN CHAMBER LEVEL ABOVE THE PETRIE PAVEMENT
Compare the direct GS-body alternative in The Petrie D-Point.
PetrieCH7.40tab: 856.2 ±.3 ¦On floor;
Petrie yQUEEN: .................... 856.2 ±.3
rJcalc:
.................................... 856.2949417436.
NomDiff: 0.095;
yQUEEN = yKING/2 + bOFFSET 18 + 2yConB = 856.2949417436 ~ 856.3:
(1693.1782168993)/2 + 21.6799079131 18 +
2(3.0129626904) = 856.2949417436.
The bOFFSET 18 part in explicit (it also
connects to the yPonB part) is the horizontally contracted
result of which vertical (ADD1.84) ArcTan½ spouse marks the casing spotting
limit (The Petrie available visual space between 1 and 4) from the
actual physical floor descending passage construction:
The details the
FIT in the edifice are somewhat and sometimes so amazingly astonishing that
one sometimes wonder if these quantities and numbers with their figures,
really, are real or just a magic dream. Those who made it really had a feeling
for it.
the physical possibility along the descending entrance
passage of finding the actual Petrie measured casing spot (pA)
connecting The 19th course floor level. See details from ENTER unless already acquainted.
What is known
here:
The above exemplified coherences makes it impossible to
reject »The Plan» as a mere coincidence.
It the rJCIRCLE Golden Section Paragon CHEOPS
RECTANGLE geometry is obviously an integrated detailed description of the
whole edifice as The Great Cheops Pyramid.
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.
WhatsUp?
PetrieCH7.41 (Queens Chamber) mentions measurement
influence from
incrustation of salts and CH7.43 salt exudation.
These are obviously long time effects (thousands of years
depending on climate conditions).
Apart from a possible sophisticated »ventilation system»
(reducing chemical attacks on the tunnel walls during long periods of time),
the ramp issue may have some alternative explanation. See THE OTHER HOLES.
Advanced
engineering.
CheopsATLASmain:
MP0: Compiled Jan2020 PART1 ¦ PART2
CHEOPS
PYRAMID CONSTRUCTION PLAN DETAILS by rJCIRCLE Complex
FULLY PETRIE CERTIFIED CALCULATED QUANTITIES
Constructive OVERVIEW QUANTITIES WITH LINKS by order of
deduction PART III
Not
much in this presentations seems to be known in modern quarters.
The
Golden Section Paragon Body
forms the unique bd=h^{2} triangle or
pyramid section here coined CHEOPS RECTANGLE:
GOLDEN SECTION EDIFICE how the unique
bd=h² pyramid triangle appears:
Through
TNED observations from the rJCIRCLE
which envelopes the GS paragon
Cheops Rectangle body, a seemingly very precise layout structure coherently
appears from the 1883 Flinders Petrie group measured CHEOPS PYRAMID:
MODERN ACADEMY IS CHALLENGED by the simple GS-paragon body fits on The Cheops Pyramid edificial design:
Investigating
the apparent CHEOPS PYRAMID¦rJCIRCLE¦GS-body
coherency, simple and straight quantitative matches show up from a basic The 7 Points xy coordinate set through the GS paragons ArcTan½! Line. We will see and study how the general whole of the
Cheops Pyramid construct is explained in detail on lengths and angles from this
coherent fit in perfect match with Petries given values and their specified
tolerances. The compilation below has links to the more detailed actual
describing sections, unless already familiar.
R = (5^½
1)/2 Point A: FULLY PETRIE CERTIFIED CALCULATED
QUANTITIES
unitINCHES rJCR internally calculated formula/term
Tunnels 26° 33 54.18 A° = ArcTan½
CASING Angle 51° 49 38.25 C° = ArcCot R^½
nValue 2.817¦2.8172301665 (yG yG)/2 = (1184.04 1178.41)/2
= 5.63/2 = 2.815
FULL DECIMALS: 1184.0412529906
1178.4067926577 = 2.8172301665
yA 665.34¦665.3382779782 GS 7
19thFLOOR y 668.15¦668.1482038706 yA+n
xA 523.06¦523.0566039073 GS 7
unitINCHES PETRIE MEASURED/calculated rJCR calculated Petrie formula/term
CASING Angle PetrieCH6.24¦32 51° 53 20 ±
1 not
(fully) connected PETRIE°* ROOF18 ¦ Petries19th ¦ 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 Petries
Casing Angle
R = (5^½
1)/2 Point B: by deductive
order: see The
G-point first
unitINCHES PETRIE MEASURED/calculated rJCR calculated Petrie formula/term*
yA 172.90 ± 0.20¦PetrieCH7.64tab 172.91¦172.9045085255 yB
(yBlimit = yConB + SIO)
xA 1517.80 ±
0.30¦PetrieCH7.64tab 1517.70¦1517.7016293661 xB
+ 18
* yConB = yPangle@H-end + yHangle@B-end = 3.0124757861
SIO = yConBoffset = nValue D
The D part is
the dValue-projection
into a xyA-vertical;
The dValue is
trigonometrically calculated from the floor construction offsets from the
G-point:.
R = (5^½
1)/2 Point G:
unitINCHES PETRIE MEASURED/calculated rJCR calculated Petrie formula/term
xP 4228 ± 2 ?¦PetrieCH7.36e 4228.00¦4227.9960057324 xG + 10R
yP 1181 ± 1 ?¦PetrieCH7.36e 1181.22¦1181.2240228242 yG nValue = yG + nValue
1181.23¦1181.2313270982 The pi-version, also below:
The P°Angle 26°
31 23 ± 5 ?¦PetrieCH7.36e 26° 31 17.48¦(26° 31 18)? 26° 31 17.486086 *ForCA
lowest ?: 26° 31 18 APPROVED only with Petries Question Mark
The H°Angle 26°
29 ± 1¦PetrieCH6.32e 26° 29¦26° 28 58.55 Hangle*
* piVersions:
Pangle = ArcTan½
ArcTan(π/[AGdistance=4135.338346])
Hangle =
ArcTan½ ArcTan(dValue/2yA(1,25)^½)
R = (5^½
1)/2 Point D:
unitINCHES PETRIE MEASURED/calculated rJCR calculated Petrie formula/term
xP 2907.30 ±
0.60¦PetrieCH7.39 2907.38¦2907.3786302 *
yP 852.60 ± 0.30¦PetrieCH7.39 852.82¦852.8245796 *see also Queen Chamber Series
* Specific Simple GS-body
paragon intersections
with xLoAnom + bO/2 and xLoBnom
+ bO + 18/2
XLoBnom =
LowerBlineNOM ....... =
XLoAnom =
LowerAlineNOM ...... = b P
xyAB = intersection point from LineAB, see Intersection Math unless already familiar.
THE D-ANGLES by deductive
order: see The
PG-point first R = (5^½ 1)/2
unitINCHES PETRIE MEASURED/calculated rJCR calculated Petrie formula/term
(B.pG)° 26° 12 50¦PetrieCH7.39¦46 26°
12 51¦26° 12 51.16 95 06 *ARCTAN
(2683R - 280R)/(F4 - 2456R)
* ARCTAN (1658.2 - 172.9)/(4534.4 - 1517.8);
Petrie gives no tolerance. He states
s39:
This, when corrected for lower signal
being 3 too high, gives
26° 12' 50" for mean angle of
both passage and gallery together., and in s46:
.. the step will be
61.1 long; and this at the angle
26° 12' 50" (by which the end
of the gallery was calculated from the plug-blocks) will be
30.08 vertically ...
(B.D)° 26° 2 30¦PetrieCH7.38¦39 26° 4 31¦26° 4 31,22 09 20 *ARCTAN [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
Petries 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 BD, 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
Petries presented [angular] values» with some minor but still acceptable deviations
within the Petrie given tolerances: no big deal.
As we already have calculated the
basic reference points from the rJCIRCLE agents as The Petrie D-point [LinD], The Petrie B-point [LinB] and The PG-point [LinPG], these angular
comparing calculations here can use a more convenient grip: Whole Number R-Multiples where these lie within the Petrie
given measures and their tolerances simplify the comparing angular values
process.
Petrie gives no direct
trigonometric formula for the angularly calculated results. So we just have to
fill in with the most simple of the Petrie given values, lengths, to check
and cross-check the valid results.
The full account for these
calculations are given in the section TP27.
R = (5^½
1)/2 Point PG:
unitINCHES PETRIE MEASURED/calculated rJCR calculated Petrie formula/term
yP 1658.20 ±
0.60¦PetrieCH7.46 1658.17¦1658.1652607385 [b1 xB]/2 + yB [ yATH + BUARM]
xP 4534.40±
0.25¦PetrieCH7.25 4555.88¦4555.8764838817 *b1 = rJCR¦b16
* SEE THE SEALING PUSH: The rJCR¦b16 agents 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:
With the mathematical geometry
thoroughly defined for the Golden
Section paragon (the GS-body), and The 1883 Flinders Petrie measured Great
Cheops Pyramid, as observed by the TNED rJCIRCLE, a first seemingly exact fit
appears between the two through The ArcTan½-line:
ENTER ¦ GS-body
HOW IT ALL STARTED PHASE
1 THE CONSTRUCT
FOUNDATION LINE
The 7 fundamental coordinate points K L M G H B A
along the entrance sloping ArcTan½ line are determined for further exact
Petrie measured quantitative comparing.
All calculations in this presentation are given through the main pyramid agent rJCR¦b16 with some support from the
ideal PetrieCR¦b58 agent.
All vertical height values are
related to the Petrie given pavement.
The rJ-reference certifies once and for all that
no possible tracing to the origin will be possible UNLESS (correspondingly) TNED familiar: The rJCIRCLE is the guide.
Concealed Construct:
PetrieCR ¦ HowStart
A Concealed Construction Plan See pyramid agent
details in Introduction
The two Pyramid Agents CR and rJ with the actual remaining
Cheops Pyramid (CP):
The actual construction plan quantities
however is made from the rJ part relative the CP¦CR part so:
All ideal INNER DESIGN GS-body Cheops Rectangle (CR) EXACT
numerical quantities the whole plan are reckoned with the rJ parts
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 2Χ21.67 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 agents
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 Petries pavement].
Such an edificial planning obviously needs some real steel sophisticated
tools.
See detailed IntroEX quantity
examples from QUEENs 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
In all (4Feb2020):
The GS-paragon Cheops Rectangle specified
as the main constructive pyramid
agent rJCR¦b16 determines
provably by quantities the corresponding measures specified by the Flinders Petrie working group
in his 1883: The geodesically measured The Great Cheops Pyramid. The corresponding
quantities prove the connection.
IntroTEF: PetrieCR An
introduction to
HOW TNED is connected
to THE 1883 FLINDERS PETRIE MEASURED CHEOPS PYRAMID
Introduction
see also further Petrie data At
the built precision
DETAILS ON THE OUTER FORM
SOME
BASIC DETAILS ON THE OUTER FORM OF THE GREAT CHEOPS PYRAMID SHOULD BE FAMILIAR;
SCHEMATICALLY:
The
leftmost below schematically iconic drawn figures
represent
the only remaining The Cheops Tourist Version
that
is left for us to visit:
remnants
of The Great (ancient named Greek Cheops) Pyramid.
PetriePLATE.11 shows a drawing of the pyramids
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 Petries 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 Pyramids
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 pyramids remaining partly eroded
staircase masonry. (The eroded parts makes a more precise [small scale] measure
out of the question).
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
TouristVersions actual Petrie measured version.
This is the actual Cheops Pyramid we
find in the Flinders Petrie based measures.
Figure a: Petries
Pyramid base in figures bc taken directly on the Petrie partly, see PetrieCH6.24, measured
casing stone slope value
51°49.
It is practically identical with The Golden Section and Cheops
Rectangle slope value angle
C° = 51°49 38,2525 = ArcTan (h/b =
1/√[R=(1+√5)/2]) = 51.82 729 237°. Also in PREFIXxSIN: ArcSin R = C°.
However: No definite direct Petrie
given such value exists presumably partly due to uncertainty issues on only
the few remaining casing blocks (also partly owing to irregularities).
The figure a-type then, will be our
only possible EXACT GEOMETRICAL candidate in any explaining ATTEMPT of the
whole Cheops Pyramid complex from the TNED point of view: the actually obtained rJCIRCLE and its claim of enveloping the
whole Golden Section Construct.
Figure d: The actual rJCR¦b16 Pyramid Agent;
Just the vertical 27.58 below Petries 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.
NATURE CHALLENGES MODERN ACADEMY
THE CHEOPS RECTANGLE From Mathematics
5 basic Laws The
Cheops Pyramid (Petrie
1883)
The Cheops
Pyramid Paragon from The Golden Section by exact Geometrical Mathematics:
See also unless already familiar GOLDEN SECTION ARITHMETICS
GOLDEN SECTION EDIFICE how the
unique bd=h² pyramid triangle appears:
The Golden
Section constant R=(√5 1)/2
with its paragon-morphological geometry shows us directly where any significant
intersections appear in the corresponding geometrically unique Cheops
Rectangle bd=h² triangle; Its tangent and slope
ArcTan[h/b=√(2/[1+√5])=1,27201965]=51.82729238°
= 51°4938.25. 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.
How it all started basic geometry illustrated
Just a simple innocent test that
suddenly
Wao. Is that really so, simple?
brightened up on its surprisingly
simple direct result:
GS-R =
(√5 1)/2 = 0.618033988..; (rJ[mJ=5.975T24KG]=7817.80)/100R = √16000.9..; (PetrieCP¦b=4534.40±0.25)/rJ
= 0.58000..
FOUND STUFF. Faulty statements are not allowed
here.
FIRST BASIC: rJ = 198.5721548 M =
7817.80 See constants in HOP.
Adopted more
precise mJ value from the ideal rJCR¦b16 value 4555.88:
mJ
= 5.9744931448 T24 KG from rJ
= 198.5665397062 M = 7817.5803033942
CENTRAL CONSTANTS: u, m(n),
m(e), h, c_{0} as given from the Instrumental
Epoch (IE 1960-1999) HOP
section.
The rJ-equation expresses the radius
of a Dmax compact TNED N3m20
deduced neutron body with the mass of the Earth
mJ=5.975 T24 KG, a sphere
with a (Dmax) density of
1.82 T17 KG/M³.
That is a sphere precisely as
illustrated NatCH:
a circle enveloping the d-corners
of the Golden Section ¦ Cheops Rectangle:
The rJCIRCLE center/origo is situated in the intersection C¦y.
With PETRIEb=4534.40 and rJ=7817.80 the relation
is
PETRIEb/rJ = 0.580009271
and the relation
rJ/100R = √16000.9049099833.
That is how it all started: WE
BEGAN TESTING THE SIMPLE NUMBERS FOR (ev.) EXACT FITS.
Testing the
precision, we adopt the two ideal Cheops Rectangle (CR) Geometries for
PetrieCR¦b58
.......... 58R√16000 = 4534.196576
~ 4534.20:
The actual ideal Flinders Petrie Cheops Pyramid with its ideal Cheops
Rectangle casing;
IDEAL: rJCR¦16 = 100R√16000 = 7817.580303
k0¦GS = √[(0.5+2/√5)²+1] = 1.7159333294 = rJ/b ; b:=rJCR¦
b16=4555.88;
rJCR¦b16
................ rJ/k0 =
(100R√16000) / √[(2/√5 + 0.5)²+1] = 4555.876484 ~ 4555.88.
EXACTLY The Same as the
b58-pyramid, but with its pyramid base situated slightly below [27.58] the
Petrie Pavement zero height reference.
Basics as calculated from the
rJ-value in NatCH.
PETRIEb
................. 4534.40
± 0.25
The comparing 1883 Flinders Petrie
measured Cheops Pyramids 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
Petries own measured values: 4534.40 ± 0.25.
The three
following iconic
CHEOPS PYRAMID
COMPLEX ILLUSTRATIONS
will help in
navigating the (tight) description:
PetrieCP PetrieCheopsPyramid:
Petrie measured the average slope of the pyramid staircase masonry as 51° 52 , with a more
narrow particular casing stone slope of 51°49 on the remaining few stones at the
pyramid base;
PetrieCR PetrieCheopsRectangle:
With the pyramids half side PETRIEb=4534.40
± 0.25 on Petries
casing slope, ideally the same as the ideal Cheops Rectangle slope
51°49 38.25 we obtain a broader and higher top pyramid enveloping Petries
staircases 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 Petries
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 Petries 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.
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
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
b_{1} b_{2} = 21.68 = bOFFSET
b1 = [rJCR¦b16 = 100R√(16000/[(2/√5 + 0.5)²+1])] = 4555.876484]
b2 = (58R√16000 = 4534.196576) The Petrie Cheops Rectangle Pyramid Agent PetrieCR¦b58 = 4534.20
b1 b2 = 21.6799079131
:
The GS-body paragon is applied on the
slightly larger same top rJ Cheops Rectangle rJCR. Its 27.58 higher/deeper
Cheops Rectangle bd=h² pyramid is then pushed vertically the same 27.58 up to
the basic pavement Petrie level and an additional half pyramid base offset
21.68 South to North INTO the
corresponding ideal Petrie Cheops Rectangle Petrie¦CR.
Result: Both pyramid agents now have the same base and casing properties
as the (for our quantitative test the remaining) Petrie measured Cheops Pyramid
Petrie¦CP;
All measures are now with respect to
the Petrie height zero preference, the Petrie pavement platform.
These arrangements establish the
construction plan quantities. The end picture shows the two pyramid agents
rJ¦CR with one and the same pyramid top and casing, where rJ has a 27.58
lower and 2Χ21,68 broader baseline situated below Petries pavement: the CR
agents 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 Petries measures.
CONTINUED
DESCRIPTION: Introduction ¦ NatCH
The
illustration below collects the basic main geometrical visual image concepts:
What we need to advance, further.
THE GOLDEN
SECTION BODY ARITHMETICS ArcTan½LINE The GS-body NatCH The Golden Section
Relation R = b/d = [√5 1]/2 = 0.618033988:
GOLDEN SECTION EDIFICE how the
unique bd=h² pyramid triangle appears:
Leftmost [R^{1}↓,
R² → , R³↑, etc.]:The Golden
Sections 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/pyramids half base.
Rightmost: Its [partial,
almost exact] resemblance with the Nautilus
Pompilius Pearl Boat Shell (sw. Pδrlbεtssnδckan).
It is here denoted with a corresponding
P for each consecutive [See deduction in GSbody]
Pn = b·R^[n1] /
√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^[n1]: The
Pyramid half base b1= R^0 = b. Next smaller GS-divided
square is R^1 for b2, then R^2 for b3, etc.
NOTE THE [50
M] DEEP WELL-TUNNEL NOT DRAWN OUT HERE with the so called Grotto in the middle
[The Cheops Rectangle Circle origo Latin:
origin, not found in the English dictionary from where the geometrical
construct is made]. Petrie [Quote] gave no measures
because of its uninviting feature. And nobody else seems to have: no specified
measured quantities are known here. Different sources give different ideas of
the actual path. See Help
ILLUSTRATIONS.
Quest:
Is there any report from Egypt 2 500 B.C. that they knew about the Golden
Section body ([5^½ 1]/2)^n structure?
A
specific search @Internet 1Jan2020 on »golden
section in ancient egypt» gives at least one PDF-based clarifying source
titled
WERE THE FIBONACCI SERIES AND THE
GOLDEN SECTION KNOWN IN ANCIENT EGYPT?, by Corrina Rossi and Christopher A.
Tout, 2002:
The conclusion is that concepts such as ϕ and the convergence to ϕ have little in common with the surviving
ancient Egyptian mathematical documents and that they are quite far from the
ancient Egyptian mentality.; The PDF-source text sometimes misses an i, here marked below:
As for the first point, it
might be suggested that the Egyptians had a geometrical concept of φ,
just as the Greeks had a geometrical concept of π, and that they tried to
approximate it using an infinite sequence of fractions. However, the first evidence of a geometrical concept of the Golden Section is to be found in Euclids 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 dont 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).
Whats your point?
IF the
Egyptians didnt know our ([√5 1]/2)^n structure in
this subject, who built
the fit?
Check the correspondences.
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.
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 Authors 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
FIRST SIMPLE OBSERVATION
A FIRST quantitative
GALLERY TEST from the rJCIRCLE fit.
Apart from the
first obvious results in (Sw.ed.) CHEOPS
REKTANGEL TabTest (Nov2017):
A First
APPROVED MEAN AVERAGE FROM THE TWO PYRAMID AGENTS
Ref.: BPOINTMain:
In determining
the B-point as 1 of The 7 fundamental
Golden Section ArcTan½ Line points,
there are two
GS-type fits: LOWER and UPPER visualizing a direct fit in the ascending
passages breadth.
The
yB-difference of these is yATH with a yBlo =
yB yATH.
Calculating the
ArcTan½ slope where it intersects the Pyramids mid vertical in Point
PG from yBlo, and using our Two Pyramid Agents respectively, we find their averaged mean
on the vertical Pyramid centre to be
1657.78.
MEAN AVERAGED RESULT : FIRST »SIMPLE» OBSERVATION
1658.20 ±
0.6, lowest 1657.60.
Approved.
Below is related even a more precise-near (1658.17) Petrie nominal value (1658.20).
See also the ROSSI2002 reference:
The ancient
Egyptians hardly knew the math as we understand it.
PETRIEpG: yPG ¦ FIRST ¦ pGconBuarm ¦ yConBUARM calc.1658
THE GREAT STEP Cheops Pyramid
Gallery ramp top,
See also THE LOST ANGLE.
Petrie does not give the direct ypGallery
value 1658.20 ± 0.6. Its
figure appears only through Petries two specified components at The Great
Step, up at the south end of the so called Grand Gallery part.
PetrieCH7.46:
.. the height of the step face is 34.92 or
35 on E. ..
.. the step surface at
the E. side of the S. doorway is 1693.2 ± .6 over the pavement.;
We calculate the difference as
1693.2 35 = 1658.2 (± 0.6)
(Some early @Internet picture photos show a
severe injured site).
rJCIRCLEcalc.:
yPG: Actual yPG math ¦ PETRIEyPG
It is clear that the rJCIRCLE Cheops
Pyramid construction plan has used a TRANSPOSITION EQUIVALENT
THE GALLERY-B-ENTRANCE-COURSE
19 CONNECTION
same recurring constants at 3
different sites between the B point (at ascending-descending) and the PG
point (at Gallery ramp top) and the 19th course level and its thickness (TCA) of the form
GALLERY RAMP END GREAT STEP 3D
drawing Here FAIRLY RECONSTRUCTED FROM GIVEN MEASURES
yATH ¦ BUARM
¦ yBlimit ¦ yPonB ¦ Fangle ¦ yBarm ¦ MiUNIT=100R ¦ bOFFSET ¦ 18
AT PG: yPG + 50R
+ yBlimit =
1693.1782168993 rounded 1693.20. Same Petrie identity.
AT PG: 50R + yBlimit =
35.0129561608 = 30.9016994375 + 4.1112567233. Same.
AT PG: yPG = [(rJCR¦b16=4555.88) xB]/2 + yB yBarm = 1658.1652607385 → 1658.17
→ 1658.2. Same.
Same. 3 different regions with the
same used exact constants defining Petries 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.
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
PetrieCH7.46 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 = 339 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
Petries 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 entrances 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 Petries measures
THE Cheops
Pyramid Inner Design CONSTRUCT IN SHORT:
The
GS-body ArcTan½-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 ArcTan½ line at point B.
The descending entrance tunnel floor B-point is
calculated from the UPPER-GS position (B upper roof) and its intersection with the
given basic ArcTan½ 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:
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.
The Great Step detailed: The MiUNIT 61.80 = 100R
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 Kings Chamber level south following
S=100R-value
marks the
transition from north to south
»EXACTLY» in
the pyramids 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 Petries
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.
Petries given tolerance ±0.2 with
34.88 allows max 35.08: we are allowed to adopt a 35.013 as below.
yV 1689.0 Petries
(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 ArcTan½ 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=h² geometry views a corresponding
IDEAL Petrie Cheops Rectangle Petrie¦CR from Petries 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=h²] 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
pyramids 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 ArcTan½ 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 ArcTan½ line specific exercise is to ASSERT and CERTIFY any person that the given
KLMGHB-points define one and the same, and only so, ArcTan½-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 ArcTan½ line
point coordinates: ArcTan½
Line ¦ GSTarCO
We relate the
Tabled-used GS-geometrical KLMGHB-xy coordinate points here from the given GS-paragons 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:
There is
another perpendicular ArcTan½-line with the same internal (in a lower
GS-fraction) GS-property as our main ArcTan½-line. These two intersect in the
point Pb where the xM-part is calculated directly as illustrated:
b5REF: GSTarCO
The triangle
ArcTan½-90°-ArcCot½ gives for two consecutive calculations from hypotenuse (b)
to longest right-angled side (b/√1.25)/√1.25
= b·0.8;
As always
sin²+cos²=1, the corresponding end shortest side will count by b·0.2
for the
ArcTan½-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
ArcTan½:
2 · 0.4b5 =
0.8b5 = My-part.
The xy-origo is related to the
pyramids 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-squares 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 ArcTan½ line: x/y=2. Mx in
total then: b2My+b4+PiLINEx, or
minus(PiLINEx
+b4 2|Gy|).
Hx = Ax ............ Hx can only be calculated with respect to a given ArcTan½
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 ArcTan½ 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.
Rough Overviewing RESULT
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)° ArcTan½ ........ 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 = Petries18th
roof. Case Closed.
There is no any
the slightest doubt that the 1883 Flinders Petrie 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,
Why there is only one unique
parallel relationship rJCR¦PetrieCR.
Then the actual connecting
explaining in
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
How Petrie Reckoned the Cheops Pyramid
Entrance.
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 Petries 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 Petries values and those emanating from the rJCIRCLE complex: The Cheops Rectangles 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=h² Cheops Rectangle pyramid construct.
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.
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
ArcTan½ 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 Pyramids 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 PHASE1 Confirming 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 Petries
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=h² Pyramid coordinates from the GS-body with our
two agents
rJCR¦b16 and PetrieCR¦b58
we arrive at the following basic
picture:
ENTER: MainConstruct
Enter
665.34 + 2.817 = 668.157 ~ 668.16:
Petries 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:
Petries 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 = 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 pyramids 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-bodys 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 Petries 19th
floor in Petries19th.
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 Petries 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 Petries given tolerance ± 1?, we
see that the difference 0.225 is negligible
like »a
perfect hit».
We cant prove it is NOT. And we cant
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 Petries
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
= 5^½ 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
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) Χ √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 Petries PangleLow 26° 31 18: ........................................ 0.51 31 40.
Pangle via GG΄/2 for nValue
................ 2.8172301665:
........... 26° 31 17.07 87 56;
Difference to Petries PangleLow 26°
31 18: ........................................ 0.92 12 44.
WITH SOME ASSISTED CERTIFIED HELP
FROM PETRIES 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.
PetrieCH7.36e describes the whole tunnels
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 = (xGxA)(1.25)^½ = [4221.8156658449 523.0566039073 =
3698.7590619376]√1.25
P° = ArcTan½
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 Petries 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
Petrie working group (1881-1883) obviously made excellent measures.
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.
Petries
measuring arrangements (StationMark) explain the details in quote PetrieCH6.31.
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 ArcTan½ 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 = ArcTan½ 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 Petries 19th floor
Selecting a lower PG-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 PG).
The end results will show us anyway how this works if at all. [It works].
RESULTING
VALUES:
n_{1} = π/√1.25
;
n_{0} = (y_{b16} y_{b58})/2
c = (10R=6.18) n_{1¦0}/2 ; = 4.7753769413
e = c·TanP° ; = 2.3831554097
PREFIXxSIN [PREFIXxSIN] : d/e=sinP°; (d/c=cosP°;
d=e·sinP°=c·cosP°);
d = e·sinP° ; = 2.1323680500
H° = ArcTan½ 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';
Petries 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:
PG n c e d H°
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 Petries 26° 29 0.00.
With Petries
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
HOW PETRIE RECKONED THE Pyramid
ENTRANCE GEOMETRY:
Petries
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.
Petries data along with
PetrieCH7.35 :
Having, then, fixed the original
position of the doorway of the Pyramid, we may state that it was at
668.2 ± .1 above the
pavement of the Pyramid;,
PetrieCH7.35.;
mean doorway height ¦ by measuring
courses ¦ 37.94 ± .17
The data for calculating the result
are
(1) levels of the 19th course by
entrance 668.30 and 705.97;
(2) floor of passage at station
mark, level 611.2
(3) which is inside the edge of the
base of the casing horizontally, 638.4;
(4) entrance passage angle at mouth 26° 29' ± 1';
(5) entrance passage height 47.26.
PetrieCH6.32.
Petrie gives no actual written formula.
But we can check and cross-check the values by using the above deduced
connections:
PetrieConPent:
PetrieCH6.32 Row32 Quote ¦
Petrie
describes the 19th course thickness with a specified tolerance at most
with
h = 37.94 ± 0.17 with (Hih38.11,
Low37.77) an end result for the floor normal e-factor above as
e = 47.26 (~47.3); PetrieCH6.32 Row56 (5) entrance passage height 47.26 gives the angles
A = 51° 53
20 ± 1 ............ =
51.88888...° = 51 + 1/1.125 °: the PetrieCH6.32 Casing surface the face of the casing;
B = 26° 29 ±
1 .................. =26.48333.... ° = 26 + 48/100 + 1/300 ° ; In
PREFIXxSIN:
How Petrie took the reckoning grasp:
e = 37.94 · cos[51+1/1.125 + 26 +48/100 = 78.36888..
]/cos[51+1/1.125] = 47.229552845.
Taking these angles for given, the
e-answer must use a lowest h = 37.964 to get
a least rounded Petrie mentioned
e = 47.26 (47.25999..).
However as
the h-value can be as high as 37.94+0.17= 38.11, a type value of
h = 37.97 does
the job for an e = 47.26 (Petrie gives no exact input parameters; as we see,
there are many to chose on).
NOTE: Petrie
explicitly names the e-part entrance passage height 47.26, NOT a Vertical Height which, through
the simplified ArcTan½ angle should read
e · √1.25
= 52.84 or 52.80068666 with PREFIXxSIN e(Vert) = e/sin(B=26° 29).
But see these
comparing results:
Petries 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 =
Petries measured 51° 53 20
From e =
42.26:
B = ArcTan½ 26°
31 23 26° 29
h = 37.9529038928 37.9585978760 37.9640039644
PetrieLowestApproved h: 37.77
PetrieNominal 37.94
PetrieHighestApproved h: 38.11
All apply.:
with A = Golden
Section Cheops Rectangle ideal in PREFIXxSIN ArcSinR = 51° 49 38.25 25 43
From e =
42.26:
B = ArcTan½ 26°
31 23 26° 29
h = 37.9292286343 37.9349502165 37.9403824145
PetrieLowestApproved h: 37.77
PetrieNominal 37.94
PetrieHighestApproved h: 38.11:
37.95 row
2 RightLeft PETRIE
37.96 row
3 RightLeft PETRIE
37.96 row
4 RightLeft PETRIE
37.93 row
2 RightRight rJ ¦ NatCH
37.93 row
3 RightRight rJ NatCH
37.94 row
4 RightRight rJ NatCH
In fact, as we
see, the latter part adopts more close to the Petrie referred nominal values
(h=37.94).
What does
that result mean or prove?
IllustrationPARTd emphasizes something like:
GIVEN THE
19th COURSE FLOOR LEVEL (y19th = 668.2 ± 0.1) with its HEIGHT or thickness (Petries
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
RESULT:
In other words,
as no notified detail interferes with the conclusion:
most exclusively and gallantly
quantitatively as this part as shown
be comprehended
as a DEFINITION of the (very gallantly performed) Petrie measuring conditions.
Petrie comes to the point entrance passage height 47.26 In Quote PetrieCH6.31 Row43.
QUOTING PETRIE
The Petrie ConPent illustrated math.
Petrie writes In Quote PetrieCH6.31 Row1 on TCA;
Petrie takes
arguments from other pyramids In Quote PetrieCH6.32 Row11.
See in
explicit: Proving the 19th Course Arithmetics:
ENTER ¦ MainConstruct ¦ SummingParts ¦ ThePush
The two
pyramid agents define the nValue subterranean 2n STRIPE in which
midpoint the Petrie vertical G-point 1181 ± 1? becomes identified:
Summing the n-value with the entrance ideal rJ-calculated A
point vertical height value 665.34, practically in a direct hit, identifies
Petries 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 Petries presented value on the
19th course floor as a nominal measure of The Petrie Measured Entrance Point.
The Gallery
point pG: The
B-point ¦ PHASE 1 ORIENTATION
GalCalcOW 2: GCOW1
GALLERY CALCULATIONS OVERVIEW part 2
THE GALLERY-B-ENTRANCE-19th
COURSE CONNECTION
The illustration clarifies how the Golden Section paragon geometry through the rJCR¦b16