Two Constants in the Garden

Introduction

In Euler's Constant and The Speed of Light I show how a pair of constants, one mathematical (gamma (y)), the other physical (c), are encoded within the first verse of the Hebrew Bible in the geometric setting provided by the Creation triangle and two internal figures, all found as numbers within the verse itself. 

Here is a brief visual summary.

 Gamma and c in the Creation Triangle

Note that;

a) these are the largest figures that will fit inside the triangle;

b) The centred triangle in the second figure is naturally rotated by 30 degrees;

c) both figures can easily be derived from word values in this text [1];

d) in each case the error is 1 part in 20800 (to 3 significant figures).

 

 

More Accurate Approximations

These encodings take advantage of the fact that numerical triangles are digital approximations of triangles in plane geometry. These constructions in plane geometry would give less accurate approximations of the constants, essentially the reciprocal numbers 3 (for c) and 0.3333. . .  (for the sq. rt. of y), because the largest internal hexagon is 6/9ths of the total area of a plane triangle and the largest internal triangle rotated by 30 degrees is 3/9ths the area of a plane triangle.

Triangle 2701 does not give the best approximations of these constants, however, as the following tables of the same constructions with other G-triangles show (only G-triangles can give these constructions). 

G-Triangle   Error in Gamma
1711 (T58)  1 in 16,900
1891 (T61)  1 in 31,900
2080 (T64)  1 in 137,000
2278 (T67)  1 in 73,400
2485 (T70)  1 in 31,300
2701 (T73)  1 in 20,800
2926 (T76)  1 in 16,100
3160 (T79)  1 in 13,300

 

G-Triangle   Error in c           
1711 (T58)  1 in 2,100
1891 (T61)  1 in 2,740
2080 (T64)  1 in 3,720
2278 (T67)  1 in 5.390
2485 (T70)  1 in 8,890
2701 (T73)  1 in 20,800
2926 (T76)  1 in 114,000
3160 (T79  1 in 16,900

 

As you can see, triangles 2080 (y) and 2926 (c) give the best estimates. These errors, both less than 1 part in 100,000, are equivalent to making an error of less than 1 cm when measuring out a distance of 1 km.

The calculations are as follows:

Gamma

y (est) = sq. rt. ((231 x 3)/2080) 

= 0.57721146. . .

y = 0.57721566. . . 

The Speed of Light 

c (est) = 2926/976 x 10^8 

= 2.99795082. . . x 10^8 ms^-1

c = 2.99792458 x 10^8 ms^-1

 

The Garden of Numbers

The Garden of Eden is one name I give to the first five verses of the NIV Bible. These contain a wealth of encoded material, displayed in several pages on this site. The code itself proclaims that it is a garden of numbers. 

Table Number in Greek

I recently discovered that both of the above triangles, and by implication the constants they hold, are encoded within the Garden. Note that the internal structures giving rise to the accurate estimations are also encoded, both within the word strings encoding the triangles.

Table Gamma and C

 

 

Summary

The most accurate estimates of gamma and c that are possible in numerical geometry are both found within the NIV Bible, surely by design!

 Bill Downie 10/5/25

 

Notes

1. These encodings (and many more), within a text that also has to make grammatical sense, could only be acheived today by something like a quantum computer. But the verse was written around 2500 years ago and has remained unaltered for over 2000 years!