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.
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.
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.
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!