I really think you were inspired posting the Conway Circle Theorem on pi day, since pi is the number derived from a circle, since there's a good estimate of pi hidden in Genesis 1.1 and since the Conway circle Theorem also involves a triangle, a form that features so much in Genesis 1.1. Something was niggling away at me, so I came back to it this morning to look for it - 7, the number of words in G1.1.
I appreciate what you're saying about the interesting fact that extending lines out from a triangle of any shape, that are equal to the opposite base length, will give a Conway circle, but I believe the major interest for students of Biblical gematria is the special case of a equilateral triangle. I've drawn one to show how all of the three principal numbers forming the architecture of Genesis 1.1 can easily be derived from a Conway circle based on an equilateral triangle.
Here is my modified Conway Circle (special case of equilateral triangle)
- Conway Circle.png (72.07 KiB) Viewed 28709 times
Here is a shortened version of the three calculations:
Starting Assumptions:
I create this special case of The Conway Circle by
a) drawing an equilateral triangle with a base of 2 units, extending the sides in each direction by the length of the opposing base, then drawing a circle that touches each line,
b) inscribing a circle within the triangle (the incircle), and,
c) circumscribing a circle touching the vertexes of the triangle (which I'm calling the outcircle).
This gives
1. an incircle radius of tan30o,
2. an outcircle radius of 2(tan30o)
3. A semiperimiter of 3 units
4. a Conway circle radius of sq.rt.(tan30^2 + 3^2)
28 (Number of letters in G1.1)
The area of the Conway circle, C, is pi x (sq.rt.(tan30^2 + 3^2))^2 = 29.32153. . .
The area of the incircle, I, is given by pi x tan30^2 = 1.047197. . .
Ratio C/I = 28 exactly = number of letters in Genesis 1.1.
7 (Number of words in G1.1)
The area of the Conway circle, C, is pi x (sq.rt.(tan30^2 + 3^2))^2 = 29.32153. .
The area of the outcircle, O, is given by pi x 2(tan30)^2 = 4.188790. . . .
Ratio C/O = 7 exactly = number of words in Genesis 1.1.
2701 (Standard value G1.1)
The area of the Conway circle, C, is pi x (sq.rt.(tan30^2 + 3^2))^2 = 29.32153. .
Now, taking that number as the radius of a larger circle,
area larger circle = pi x 29.32153. . ^2 = 2700.991. . . . = 2701 = standard value Genesis 1.1.
The error here is only 0.0003%, or 1 part in 300,000;
So a modification of the special case of The Conway Circle, a 21st Century theorem, generates the three principle numbers defining Genesis 1.1.
Note: one number links all three Genesis numbers. This is 29.32153. . . the area of the Conway circle and the radius of the larger circle with area 2701.
