M22 #3.5: lix number codes
Imagine building a simple rectangular workshop with a flat ceiling using as dimensions
the square roots of (213x .009) x 4, 21, 9, 25, 16, 20 and 5.
Imagine next to your workshop constructing a simple rectangular shed with a gabled ceiling using as dimensions
the square roots of 4, 5, 6, 7, 8, 9, 10, 11, 13 and 15 each multiplied by (28 x .03).
Imagine fitting one inside the other.
If you quickly scan this presentation, jumping over numbers and formulas in a 20th Century rush to get to the ergo sum, the punch line, you will miss the point and it’s far too good a point to miss. Numbers and Formulas generating these dimensions are the message but don’t take my word or anyone else’s. Confirm them yourself. Read each step and check the simple arithmetic as you go. It won’t take long and by the end of this brief, if nothing else, you will have a deeper appreciation for what motivated the designers and builders of the Great Pyramid at Gizeh.
If you’ve arrived here from a direct link, unfamiliar with lix measure and its application to the “Hi Phive”, King’s Chamber, you don’t have to go here first but it will put the following information into context.
(n.5 = square root n)
5.5 x .5 = 1.1180339887 = 1.25.5
5.5 x .5 + .5 = 1.6180339887 = phi
Four dimension codes were discover in the early 1980′s by Joseph Edward Batter after we completed the machine array, the lix grid cross section of the Great Pyramid at Gizeh. Following his death in 1994 i collated some of the basic elements of our collaboration and opened the web pages, “the lix unit”, in late ’96,
followed by “lixcaliber” in 1998.
1 lix = 1.001006 feet
In January, 2008, while reworking the lix number code of the Hi Phive Chamber, I suddenly realized the squared dimensions shared another common factor, [G], the sum of the squared dimensions: 7372.8 divided by 100.
Looking back it now seems obvious. In fact the answer was there for all to see ever since Joe first deciphered the dimension codes and throughout the dozen years they’ve been posted on the web. My deep chagrin for having found 73.728 in 2003 without realizing what it meant is slowly fading.
With [G] resolved it seemed likely the module would apply to other areas of the Great Pyramid so i went to the Google to find “Queen’s” chamber dimensions. I knew the width was the same as the Hi Phive width, (17.17300207 lix) however as it was not part of our initial investigation, i had no idea what the other dimensions were.
On Tim Hunklers Pyramid site i found Simpson1 had already deduced a part of the “King’s” chamber sequence using a Unit Dimension of 103.03 primitive inches, (half the width). More exciting was his discovery of a portion of the Queen’s chamber sequence based on a unit dimension of 92.173077+ primitive inches, (half the side wall height) and the square roots of 4, 5, 6, 7, 9, 10, 11, and 15.
As you will soon see, had Simpson employed a unit dimension of 92.16, ( 9.62),
the chambers of the Great Pyramid would have become instantly transparent:
92.16 x 1.25.5 = 103.0380124 lix = Hi Phive chamber, perimeter.
92.16 x 20 = 1843.2 = Hi Phive chamber, cubic diagonal squared.
1Simpson code from “Authorship and Message of the Great Pyramid” Julian T.Grey 1953
The dates at the beginning of each of the following sections mark major steps along my path leading to the “Numerical Source of Great Pyramid Chamber Dimensions”.
02 20 ’08
No Queen was ever interred in the “Queen’s” Chamber. As with the Hi Phive, “King’s”, Chamber the name should reflect the purpose behind the design and is hereafter referred to as the “Point Phive” Chamber.
From Tim Hunklers list of Pyramid measurements:
Simpson deduced a number sequence in the Chamber using a Unit Dimension, a module,
of 92.173077 + “primitive” inches, half the side wall height. He discovered:
| side wall height | UD x 2 |
| width | UD x 5.5 |
| length | UD x 6.5 |
| apex height | UD x 7.5 |
| end wall diagonal | UD x 3 |
| floor diagonal | UD x 10.5 |
| side wall diagonal | UD x 11.5 |
| cubic diagonal | UD x 15.5 |
Note: floor diagonal and side wall diagonal are switched. Corrected below.
Squaring the sequence factors produces the series: 4, 5, 6, 7, 9, 10, 11, and 15.
I converted Simpson’s unit dimension to feet: 92.173077 / 12 = 7.68108975
and multiplied it by 5.5 to determine his chamber width in primitive feet = 17.175438+.
Compare with Rutherford’s width of the Hi Phive chamber: 17.17216083 primitive feet.
Knowing that the width of both chambers are equal, i divided the true width, 17.17300207 lix by 5.5
and found the unit dimension, half the side wall height, is exactly 7.68 lix.
17.17300207 / 5.5 = 7.68000000125
Point Phive chamber width = 7.68 x 5.5 = 17.17300207 lix = [Y], [Y2] = 294.912
7.68 = (28 x .03)
7.682 x 10 = 589.824 = side wall diagonal squared = [Y2] x 2
Applying the true module, 7.68 lix to Simpson’s code reveals the original design specifications of the Point Phive chamber. Following the pattern of the Hi Phive number code i squared the lix dimensions and divided the results by [G], revealing the side wall proportion code.
The squared dimensions are multiplied by 5 to illuminate the [Y2] and [G] code and their source in Hi Phive .
[G] / 7.68 = 9.6
9.63 = 884.736 = cubic diagonal squared
Point Phive Chamber: lix dimensions
| line | formula | lix dimension = N | N2 | N2 / [G] |
N2x 5 | = n[Y2] | = 4n[G] | = Hi Phive |
| height: side wall | 7.68 x 4.5 | 15.36 | 235.9296 | 3.2 | 1179.648 | 4 | 16[G] | [U2] |
| width | 7.68 x 5.5 | 17.17300207 | 294.912 | 4 | 1474.56 | 5 | 20[G] | [T2] |
| length | 7.68 x 6.5 | 18.81208122 | 353.8944 | 4.8 | 1769.472 | 6 | 24[G] | [T2] + [Y2] |
| height: apex | 7.68 x 7.5 | 20.31937007 | 412.8768 | 5.6 | 2064.384 | 7 | 28[G] | [T2] + 2[Y2] |
| ? | 7.68 x 8.5 | 21.72232032 | 471.8592 | 6.4 | 2359.296 | 8 | 32[G] | 2[U2] |
| diag: end wall | 7.68 x 9.5 | 23.04 | 530.8416 | 7.2 | 2654.208 | 9 | 36[G] | [T2] + [U2] |
| diag: side wall | 7.68 x 10.5 | 24.28629243 | 589.824 | 8 | 2949.12 | 10 | 40[G] | 2[T2] |
| diag: floor | 7.68 x 11.5 | 25.47167839 | 648.8064 | 8.8 | 3244.032 | 11 | 44[G] | 2[T2] + [Y2] |
| diag: cubic | 7.68 x 15.5 | 29.74451209 | 884.736 | 12 | 4423.68 | 15 | 60[G] | 3[T2] |
| totals | 195.92925659 | 4423.68 | 60 | 22118.4 | 75 | 300[G] | 15[T2] |
(n[G]/5).5
eg) floor diagonal = (44[G]/5).5 = (648.8064).5 = 25.47167839 lix
All the dimensions of the Point Phive chamber are derived from combinations of the squares
of the width, length and ceiling diagonal of the Hi Phive chamber: [Y2], [U2] and [T2]
Hi Phive dimension = (n[G]).5
eg) length = 34.34600414 lix = [U]
[U2] = 1179.648 = 16[G]
(16[G]).5 = 34.34600414
Point Phive dimensions = (n[G]/5).5
eg) side wall height = (16[G]/5).5 = 15.36 lix
15.362 x 5 = [U2]
03 13 ’08
Simpson’s “Queen’s” chamber, square root series: 4, 5, 6, 7, 9, 10, 11, 15, + = 67,
is missing at least one number: 8, while 15 is out of position.
Beginning at the top of the 4n[G] column each dimension increases by 4[G] with a gap of 8[G]
between the height apex, 28[G] and the end wall diagonal, 36[G].
Extrapolating backwards: (32[G]/5).5 = 21.72232032 lix = (7.68 x 8.5)
The location of this line is unknown at the moment however it is likely in the gabled ceiling where the stones overhang the walls. The number is connected to the Hi Phive chamber length:
21.72232032 x 2.5 = 34.34600414 = [U]
The sequence now resolves itself, unfolding as pairs, each total 15 around the cubic diagonal:
4, 5, 6, 7, 15, 8, 9, 10, 11
4 + 11, 5 + 10, 6 + 9, 7 + 8 = 60 + 15 = 75
In the Hi Phive chamber the lix number code also unfolds as pairs.
Each total 25 around the cubic diagonal:
4, 21, 9, 25, 16, 20, 5 + = 100
03 14 ’08
Thirteen:
Simpson’s code is missing another prime dimension, the diagonal of the largest rectangle in the chamber.
At half the width, down the centre, from the ceiling apex to the opposite floor:
Triangle:
floor length = 6.5 x 7.68
apex height = 7.5 x 7.68
diagonal = 13.5 x 7.68
| line | formula | lix dimension = N | N2 | N2 /[G] | N2 x 5 | = n x [Y2] | = 4n[G] |
| ? | 7.68 x 12.5 | 26.60430040 | 707.7888 | 9.6 | 3538.944 | 12 | 48[G] |
| diag: apex | 7.68 x 13.5 | 27.69063379 | 766.7712 | 10.4 | 3833.856 | 13 | 52[G] |
| total | 54.29493419 | 1474.56 = [T2] | 20 | 7372.8 | 25 | 100[G] |
Adding 8, 12, and 13 to the sequence raises the sum of the Point Phive code to 100,
the same as Hi Phive, 33 more than Simpsons original 67.
Hi Phive chamber volume, 11324.6208 cubic lix = 19.23 x 1.6,
minus Hi Phive perimeter squared: 10616.832 = 707.7888 = 19.23/ 10
The sum of the 9 dimensions in the (N2x 5) column = 22118.4 = 300[G]
Adding 12 and 13 (above): 7372.8 + 22118.4 = 29491.2 = 100[Y2]
[Y2] + [U2] + [T2] = 2949.12
seven / eleven:
The sum of the 7 “Hi Phive” squared dimensions = 7372.8 = [G] x 100
The sum of the 11 “Point Phive” squared dimensions, (N2 column), = 5898.24 = 7.682 x 100
7372.8 / 5898.24 = 1.25
04 03 ’08
Point Phive Triangles
Wall and floor triangles produce more power of .5 factors when the chamber floor is divided in quarters:
And the end wall is folded in half:
04 05 ’08
The power of point phive, 7.68 lix and Hi Phive chamber dimensions
| [Y] = 5.5x 7.68 | = 17.17300207 lix |
| [X] = 26.25.5x 7.68 | = 39.4829094 |
| [W] = 11.25.5x 7.68 | = 25.75950310 |
| [V] = 31.25.5x 7.68 | = 42.93250517 |
| [U] = 20.5x 7.68 | = 34.34600414 |
| [T] = 25.5x 7.68 | = 38.4 |
| [S] = 6.25.5x 7.68 | = 19.2 |
The Numerical Source of Great Pyramid Chamber Dimensions
3 Unit Dimensions for both Chambers:
[G] = (213 x .009) = 73.728 lix, [Y] = (215 x .009).5 = 17.17300207 lix, (28 x .03) = 7.68 lix
| Hi Phive chamber line | lix dimension | proportion code | point phive code | |
| = n[G] | (n[G]).5 = | = n x [Y] | = n x 7.68 | |
| width, [Y] | 4[G] | 17.17300207 | 1 | 5.5 |
| diag N wall, [X] | 21[G] | 39.34829094 | 5.25.5 | 26.25.5 |
| diag W wall, [W] | 9[G] | 25.75950310 | 1.5 | 11.25.5 |
| diag cubic, [V] | 25[G] | 42.93250517 | 2.5 | 31.25.5 |
| length, [U] | 16[G] | 34.34600414 | 2 | 20.5 |
| diag ceiling, [T] | 20[G] | 38.4 | 5.5 | 25.5 |
| height, [S] | 5[G] | 19.2 | 1.25.5 | 6.25.5 |
| Point Phive chamber line | lix dimension | proportion code | point phive code | |
| = n[G] | (n[G]/5).5 = | = n x [Y] | = n x 7.68 | |
| half width | 5[G] | 8.58650103 | .5 | 1.25.5 |
| diag quarter floor | 11[G] | 12.73583919 | .55.5 | 2.75.5 |
| height: side wall | 16[G] | 15.36 | .8.5 | 4.5 |
| width | 20[G] | 17.17300207 | 1 | 5.5 |
| diag half end wall height | 21[G] | 17.59709066 | 1.05.5 | 5.25.5 |
| length | 24[G] | 18.81208122 | 1.2.5 | 6.5 |
| diag half floor width | 26[G] | 19.58023493 | 1.3.5 | 6.5.5 |
| height apex | 28[G] | 20.31937007 | 1.4.5 | 7.5 |
| diag half floor length | 29[G] | 20.67903285 | 1.45.5 | 7.25.5 |
| ? | 32[G] | 21.72232032 | 1.6.5 | 8.5 |
| diag half end wall apex | 33[G] | 22.05912056 | 1.65.5 | 8.25.5 |
| diag end wall | 36[G] | 23.04 | 1.8.5 | 9.5 |
| diag side wall | 40[G] | 24.28629243 | 2.5 | 10.5 |
| diag floor | 44[G] | 25.47167839 | 2.2.5 | 11.5 |
| diag cubic mid flr height | 45[G] | 25.75950310 | 2.25.5 | 11.25.5 |
| ? | 48[G] | 26.60430040 | 2.4.5 | 12.5 |
| diag apex | 52[G] | 27.69063380 | 2.6.5 | 13.5 |
| ? | 56[G] | 28.73592873 | 2.8.5 | 14.5 |
| diag cubic mid flr apex | 57[G] | 28.99136423 | 2.85.5 | 14.25.5 |
| diag cubic | 60[G] | 29.74451209 | 3.5 | 15.5 |
| ? |
Samples from four Point Phive chamber lix unit codes:
04 20 ’08
The end walls of both chambers are overlaid and six main diagonal lines applied,
three on Point Phive, two on Hi Phive and at the top, 1.05.5 joins one chamber with the other:
Triangle: .05.5 x 1 x 1.05.5
3.84 x 17.17300207 x 17.59709067
[Y] x .8.5 = 15.36, [Y] x 1.25.5 = 19.2, [Y] x 1.8.5 = 23.04
3.84 x 4 = 15.36, 3.84 x 5 = 19.2, 3.84 x 6 = 23.04
multiples of 1.92:
1.92, 3.84, 5.76, 7.68, 9.6, 11.52, 13.44, 15.36, 17.28, 19.2, 21.12, 23.04, 24.96
25 x .03 = .96, 26 x .03 = 1.92, 27 x .03 = 3.84
28 x .03 = 7.68, 29 x .03 = 15.36, 28 x .32 = 23.04
09 14 ’08
Relationships between the Point Phive and Hi Phive chamber dimensions
Point Phive side wall diagonal = [Y] x 2.5
Point Phive cubic diagonal = [Y] x 3.5
Hi Phive ceiling diagonal = [Y] x 5.5
Point Phive wall height = [Y] / 1.25.5
Hi Phive wall height, [S] = [Y] x 1.25.5
[Y] x 1.8.5 = 23.04 = end wall diagonal
[S] x 1.8.5 = 25.75950310 = [W] = west wall diagonal
[W] / 23.04 = 1.25.5 = phi – .5
Point Phive side wall height, mid cubic diagonal = [W]
triangle: 15.362 + 20.679032852 = 663.552 = [W2]
11.25.5 x 7.68 = 25.75950310 = [Y] x 1.5 = [W]
[W] x Hi Phive length, [U] = cubic diagonal squared
25.75950310 x 34.34600414 = 884.736 = 9.63
38.4 x 23.04 = 884.736
ceiling area [Y] x [U] = side wall diagonal squared
17.17300207 x 34.34600414 = 589.824 = 7.682 x 10
side wall height, 15.36 + 23.04 = 38.4 = [T], ceiling diagonal
15.36 x 23.04 = 235.9296 = length squared
15.36 x 19.2 = 294.912 = width squared
19.2 x .8.5 = 17.17300207, x .8.5 = 15.36
Hi Phive volume = 11324.6208 = [G] x 153.6
cubic diagonal squared, [V2] / 15.36 = 1843.2 / 15.36 = 120
In both chambers, the sum of the squared dimensions divided by the cubic diagonal squared:
Point Phive, (9 dimensions), 4423.68/ 884.736 = 5
Hi Phive, (7 dimensions), 7372.8 / 1843.2 = 4
4423.68 / 1843.2 = 2.4
884.736 / 737.28 = 1.2
Point Phive, (N2 x 5) column:
(10), 2949.12 + (11) 3244.032 + (15), 4423.68 = 103.03801242
Hi Phive chamber: [W] + [U] + [V] = 103.0380124 = [M] = horizontal perimeter = [Y] x 6
02 05 ’09
a simple calculator exercise for acquiring various key lix chamber dimensions:
1.25.5 = 1.1180339887 = phi – .5
(23 x 3)
24 / 1.25 = 19.2 = [S] = Hi Phive chamber: height
24 / 1.252 = 15.36 = Point Phive chamber: side wall height
24 / 1.11803398873 = 17.17300207 = [Y] = Hi Phive and Point Phive chambers: width
(22 x 32)
36 / 1.11803398873 = 25.75950310 = [W] = Hi Phive: end diagonal
36 / 1.11803398874 = 23.04 = (36[G]/5).5 = Point Phive chamber: end diagonal
36 / 1.11803398875= 20.60760248 = [A] = magnum module
36 / 1.11803398876 = 18.432 = [V2] / 100
36 / 1.11803398878 = 14.7456 = [T2] / 100
36 / 1.118033988710 = 11.79648 = [U2] / 100
(24 x 3)
48 / 1.1180339887 = 42.93250517 = [V] = Hi Phive: cubic diagonal
48 / 1.11803398872 = 38.4 = [T] = ceiling diagonal
48 / 1.11803398873 = 34.34600414 = [U] = length
(3 x 5)2
225 / 1.11803398877 = 103.0380124 = Hi Phive perimeter = [M]
225 / 1.11803398878 = 92.16 = 9.62
225 / 1.118033988710 = 73.728 = [G]
225 / 1.118033988712 = 58.9824 = 7.682
…….something’s afoot……
The rediscoveries of the lix unit, the scale lixcaliber, the dimensions of Hi Phive, [G] and Point Phive are the result of nearly two lifetimes of attention. Much is owed to the Master Surveyors who marked the lines before our time and even more to Pythagoras and his teachers.
A paper structure of equal volume could be built beside the Great Pyramid from all the speculative works to reference its grande design. Bairn of pi and phi, “lix” dimensions are eternal; here long before the first Myths were recorded; here well after the last ones are gone to dust. Embedded in the Stone hearth of Phive resides the planetary scale “lixcaliber“, not as Arthurian weapon, tool for Passion, War and Division but as Arthurian ideal, instrument of Compassion, Reason and Understanding. In another age people were inspired enough to strive together for a generation to dress and seal their knowledge of “Earth Measure” inside a crystalline mountain 481.9660111 lix high. They clearly intended rediscovery, whether by this era remains to be seen.
04 13 ’08
stephen langton goulet
© 2008 – 2011
stephen langton goulet
all rights reserved
updated: August, 2011
