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  Introduction

A small booklet1 published in 2000 by this author reveals an intriguing discovery, or quite possibly a re-discovery of ideas from an earlier time, that allowed tabularization of the Fibonacci series into self-limiting columns and rows of one, two and three digit numbers. A process termed number distillation2 that is often referred to as "the casting out of nines" is responsible for, and allows, the all-important self-limiting aspect of the tables that were created.  The column and row sums, as well as specific numerically marked area summations, proved in most cases to provide historically significant numbers that were oft times repeated in other of the tables. Table-1, the parent table that is included herein allows the reader a glimpse of the power of such tables in providing numbers of historical significance, all of which seem to be a part of Nature's grand design.

One of the most exciting discoveries was that several of the tabular summations numerically matched major external measurements of the Great pyramid as measured in feet.   Ratios formed of certain sums proved to be very close approximations for Pi (p) and the Golden Ratio (j).     Some tabular summations from other of the tables numerically matched geological measurements of physical items such as earth density, axial rotation speed and rotational energy.


Writer and reviewer Gary Val Tenuta best captures the feelings of the author about his findings when he states: "Turbeville has apparently discovered something new under the sun. Or has he? While it may be new to us, as we stumble along seeking answers to the mysteries of the universe within the current scientific paradigm, the implications of the stunning correlations discovered by Turbeville suggest the possibility that he has rediscovered something that was known to the ancients but which was lost over the millennia. What we may have here is an archaeological find uncovered without ever having wielded a single stroke of pick-ax or shovel."


Table Format 

Table-1 is a natural formation of 216 Cells arranged in 9 rows of distilled Fibonacci numbers in 24 columns, where each successive row is obtained by multiplying the row number by each respective top row factor and distilling. This limited grid pattern repeats itself when distillation is continued in either the X or Y direction.

 

Table-1 Notes

 

• Baseline Width of the Great Pyramid  = 1188 – 2( 216 )  =  4( 189 )  = 756 feet.
• The total sum minus the sum of all the nines = 1188 –  9( 48 )  = 756 feet.
• The digit sum of the two central dark gray rectangles  =  216   
                   Also, the  total number of  table cells  (9 x 24) =  216 
• The digit sum of the perimeter digits (light gray cells) =  612   
    The Apothem length (distance from apex to baseline mid-point) @ 612 feet. 
• The sum of the forty border nines (dark gray 9’s on gray cells) = 9(40) = 360   
    Archaic value for the number of days in a year  and degrees in a circle 360
• Pyramid scale size to the Earth = (1 : 43200)   Þ   2(216) = 432  = Base ten factor. 
• Pyramid  Pi Factor (p_p) =  594 / 189  =  22/7 =  3.142857  
• Pyramid Height = Base Area Perimeter / 2p_p = (4 x 756 ft) / 2(22/7) = 481.1 ft. 
  Pyramid Height = Base Area / Total Sum Table-1 = (756 ft)² /  1188 ft  =  481.1 ft.
• Golden Ratio @ Apothem / half-width @ Ö ((481.1 ft)² + (378 ft)² ) /  378 ft =   
  Golden Ratio @  1.618609               0.036% error                                                                                                                                                                                

The Royal Cubit & Golden Mean

 

If each of the digits in the first twelve cells of Row-1 (Table-1) is divided by the digit that precedes it,
there will be eleven rational terms that added sum to 20.617857

1/1 + 2/1 + 3/2 + 5/3 + 8/5+ 4/8 + 3/4+ 7/3 + 1/7 + 8/1 + 9/8  = 20.617857 = 20.618

Limiting this number to three decimal places provides as much significance as the
number need have when one assumes that a unit equivalent to the English inch might
have been intended when a value was selected for the Royal Cubit.


     Tabular Ratio Summation Value of the Royal Cubit = 20.618 inch

 

         W.M. Flinders Petrie in his historic work, The Pyramids and Temples of Gizeh 3 provides us a value for the Royal cubit that has become the generally accepted value. 
i.e.  Royal Cubit = 20.620 ± 0.005 inches   (British Imperial Units)

                                                             

                                   
Could the string of ratios that produce this historical value really be the source of the Royal Cubit? The possibility is supported by the fact, partially displayed in Table-1 Notes, that tabularization of the Fibonacci series by the process of distillation provides a wellspring of numerical knowledge for seekers of historic truths and on occasion will reveal a "new glimmer of light". Interestingly, the pivotal value for each column and row of Table-1 is the product of this ratio string,   i.e. the number nine. 

              

             1/1 × 2/1 × 3/2 × 5/3 × 8/5 × 4/8 × 3/4 × 7/3 × 1/7 × 8/1 × 9/8 =  9

 

When each of the digits of the string is multiplied by the digit that follows it,   and then distilled, the distilled product sum of the eleven terms will be 54.

 

        1×1 + 2×1 + 3×2 + 5×3 + 8×5 + 4×8 + 3×4 + 7×3 + 1×7 + 8×1 + 9×8  =  54
   1  +   2  +   6  +  6  +   4   +   5   +  3   + 3    +  7   +  8   +  9  =  54 

 

         Golden Mean  @ Ö(54 / 20.618) = 1.618354  @ 1.618034 _{true value}   (0.02% error)    

  1 "A Glimmer of Light from the Eye of a Giant": Tabular Evidence of a Monument in Harmony with the Universe" - ISBN 1-55212-401-0,  www.trafford.com/robots/00-0065.html 

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