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Joseph Turbeville

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An Amazing Application of  Nature’s Numbers
~ Case Two ~
Hand Count Method for Distilled Fibonacci Numbers Provides Hidden Keys to Major Design Elements of the Great Pyramid

Identify the fingers of the left hand according to the first four terms of the Fibonacci series. i.e. 1, 1, 2 & 3, starting with the forefinger as indicated in the figure above. Then in a somewhat similar fashion, identify the fingers of the right hand with the second four terms (after distillation of the double-digit numbers), i.e.,
5+8 = 13 Þ 4, 4+8 = 12 Þ 3, 3+4 = 7 starting with the little finger. 

Some may find it helpful in the beginning to mark the numbers on their fingertips to simplify the following summations. The zero and the seven Identify the left and right thumb respectively. The zero is considered a placeholder and the seven as a pivotal number.  When the thumbs and the fingers are placed together tip to tip as shown below, the mirror image two digit numbers listed in the following table can be read from either left to right, or right to left, when looking into the palms.

A-A Case Two - Table 2


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The digit sum of the four fingers on the left hand (7) and digit  sum of the four fingers on the right hand (20) have a total sum of (27). Also the total sum of all five digits on the right hand is (27).

The square root value of the Golden Ratio ÖPhisub-1   i.e. (Öj1),  that is found in the Great pyramid is found herein by dividing the (L Û R) product of the 4-Finger sums by the (LR + RL) ring-fingers sum). i.e.
7 x 20 = 140 
Þ and  140/110 = 14/11 = 1.272727··· = Öj1
Pyramid Phi ( j1)= (14/11)2 = 1.619835   (0.11 %  error)
Pure math value of Golden Ratio Phi (
j) = 1.618034

Pyramid Pi (pp) = 4/Öj1
= 4/(1.2727) = 22/7 = 3.142857


The four-finger summation number (297), when multiplied by the square root of our Pyramid Phi factor Öj1  yields a historically significant number that is numerically equal to the half-width of the Great pyramid as measured in feet. In a similar manner, this half width obtained (378 ft.), when multiplied by Öj1 reveals a most probable design height, and the design height value when multiplied by Öj1 yields the apothem value, i.e.

Half-width = Öj1 x 297 ft. =  (14/11) x 297 = 378 ft.

Design height = Öj1 x 378 ft. = (14/11) x 378 ft = 481.1 ft.

Apothem length =Öj1 x 481 ft. = (14/11) x 481 ft. @ 612 ft.

These three external measures for the Great pyramid are the same values the author obtains by tabularization of the Fibonacci series as first discussed in his book, A Glimmer of Light from the Eye of a Giant. - ISBN 1-55212-401-0


The inverse tangent of the rise over the run provides the slope angle of the pyramid,  i.e.
inverse tan. of (height / half width).
Slope angle = Invtan (481.1' / 378') = 51°.8433  @ 51° 51 min.


The hand count revelation disclosed here, provides a unusual calculation to obtain the pyramid slope angle. It uses the left and right hand four-finger summations of the Fibonacci numbers in a (product / sum ratio).   i.e. (p/s).  This provides an extremely accurate measure for a tenth part of the  baseline slopeangle of the Great Pyramid.   i.e.

Slope Angle = 7 x 20 = 140,  and the sum  =  7 + 20  =  27
(p/s) = 140/27 = 5.185185    10(5.185185) = 51.85185
This number, if assumed to be a measure in degrees, is a reasonably precise  measure of the slope angle for each face of the Great pyramid.
Slope Angle = 51°.85185 or 51°51' 07" @ 51° 51' 


The left and right hand, distilled Fibonacci number summations, have a product that when divided by the ring finger summation provides a precise value for the Royal cubit. as measured in feet.  i.e.  

Royal Cubit = (7 ft.) x (27 ft.)/(110 ft.) = 1.7181818×××× feet 

(1.71818×××feet / RC) x (12 inch / feet) = 20.61818 inch / RC


The four-finger sums of each hand provide a left times right hand product that when multiplied by Pyramid Pi(pp) provides the numerical value of the Great pyramid's baseline width, as measured in Royal Cubits.

Great Pyramid base-line width = (7 x 20) x (22/7) = 440 RC

440 Royal Cubit x (1.71818××× feet/ RC)  =  756 feet


2003, Joseph Turbeville - All rights reserved