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Triangles are fundamental in the history of Mathematics. The first proposition in Euclid's Elements (written around 300 BC) was about how to construct an equilateral triangle.
The Pythagorean Theorem relating the lengths of the sides of a right triangle is one of the most famous theorems in mathematics. It's from around 500 BC.

Given the centrality and antiquity of the study of triangles, it is surprising that a new beautiful theorem relating to triangles was still waiting to be discovered in the 21 century: Conway's Circle Theorem.
Now here's a question for those who love studying the alphanumeric and geometric patterns in Scripture - Can you find any way this theorem relates to our studies?

Happy hunting!

Interesting problem!

If we construct an equilateral triangle to give the simplest case, and make each side 2 units, then we can first find the centre of the incircle by drawing lines from each vertex to the centre of each side, then inscibe the circle. The triangle will have three internal angles of 60o. Drawing a line from the centre of the incircle to any vertex, gives a right-angled triangle, with one of the sides being 1 unit in length and 30o as the smallest angle. So we have, from Wikipedia,

radius Conway circle (R) = sq.rt.(r^2 + s^2)

r = inradius = tan 30 = .57735. . .
s = semiperimeter = (2 + 2 + 2)/2 = 3

Solving, we have

R = sq.rt. ((.57735..)^2 + 3^2) = 3.05505. . .

The radius ratio is then R/r = 3.05505../.57735... = 5.2915. . .

The ratio of the areas of each circle is then piR^2/Pir^2 = 29.32152. . ./1.047197. . . 28

This of course is the number of letters in Genesis 1.1.

Addendum:

The relative area of the Conway circle, 29.32152 units^2, is the radius of a circle of area 2701 units^2

This is pi day too!

bluetriangle wrote: Sat Mar 14, 2026 3:29 am Interesting problem!

If we construct an equilateral triangle to give the simplest case, and make each side 2 units, then we can first find the centre of the incircle by drawing lines from each vertex to the centre of each side, then inscibe the circle. The triangle will have three internal angles of 60o. Drawing a line from the centre of the incircle to any vertex, gives a right-angled triangle, with one of the sides being 1 unit in length and 30o as the smallest angle. So we have, from Wikipedia,

radius Conway circle (R) = sq.rt.(r^2 + s^2)

r = inradius = tan 30 = .57735. . .
s = semiperimeter = (2 + 2 + 2)/2 = 3

Solving, we have

R = sq.rt. ((.57735..)^2 + 3^2) = 3.05505. . .

The radius ratio is then R/r = 3.05505../.57735... = 5.2915. . .

The ratio of the areas of each circle is then piR^2/Pir^2 = 29.32152. . ./1.047197. . . 28

This of course is the number of letters in Genesis 1.1.

Addendum:

The relative area of the Conway circle, 29.32152 units^2, is the radius of a circle of area 2701 units^2

This is pi day too!

Happy Pi day Bill! Do you have any special plans for 1:59:26 this afternoon?

I love your attempt to answer this question. After I wrote it, I noticed that the perfect symmetry of the figurate triangles (being equilateral) doesn't capture the most interesting fact of Conway's theorem, that the extended lines match the lengthy of the opposing side for ANY triangle. But Conway's picture is so beautiful and the theorem so interesting that I wanted to share it.

Peace!

Richard

RAMcGough wrote: Sat Mar 14, 2026 7:36 am
Happy Pi day Bill! Do you have any special plans for 1:59:26 this afternoon?

It's in the past here. I guess I'll have to wait until 6.53.58 now.

RAMcGough wrote: Sat Mar 14, 2026 7:36 am I love your attempt to answer this question. After I wrote it, I noticed that the perfect symmetry of the figurate triangles (being equilateral) doesn't capture the most interesting fact of Conway's theorem, that the extended lines match the lengthy of the opposing side for ANY triangle. But Conway's picture is so beautiful and the theorem so interesting that I wanted to share it.

Oh, is that not it? Or was it an open ended question? I think it's impressive that you can easily derive 2701 and 28 pretty much exactly from the special case of the theorem. The error in the calculation of 2701 is less than 1 part in 300,000. The calculation of 28 is exact.

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)


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.

All of this is excellent research when working on a flat-plane. But it is just a drop in a ocean when considering all the types
of geomtry we know about: Non-Euclidean, Elliptical, Hyperbolic, Analytical, Differential, Topology, Projective, Algebraic geometry, not to
mention all the forms of calculus, string theory, Quantum entanglement, quantum mechanics\physics, etc and etc.


For me, I am waiting on the New Heavens and New Earth.


106 + 560 + 000 = 666


The number 2701 occupies 165 + 166 + 167 + 168 = 666



the dust of the earth כעפר הארץ (Gen 28:14) 666



Gen 28:14 And thy seed shall be as the dust of the earth,
and thou shalt spread abroad to the west, and to the east,
and to the north, and to the south: and in thee and in thy
seed shall all the families of the earth be blessed.




In the KJV the name Jesus occurs 973 times.


Praise the LORD!

Proverbs 8:27
When he prepared the heavens, I was there: when he set a compass upon the face of the depth:


I was there שם אני (Hebrew Text) = 401


the Word Jesus the Aleph and Tav (1 + 400) = 401




Rom 8:39 Nor height, nor depth, nor any other creature, shall be able to separate us from the love of God, which is in Christ Jesus our Lord.

the love της αγαπης (Greek) 801

the Word Jesus the Alpha and Omega (1 + 800) = 801



Gen 1:2 And the earth was without form, and void; and darkness was upon the face of the deep.
And the Spirit of God moved upon the face of the waters.



the Spirit of God רוח אלהים (Gematria Value) 300
of the earth 300x

KingJamesMath wrote: Sun Mar 15, 2026 6:37 am All of this is excellent research when working on a flat-plane. But it is just a drop in a ocean when considering all the types
of geomtry we know about: Non-Euclidean, Elliptical, Hyperbolic, Analytical, Differential, Topology, Projective, Algebraic geometry, not to
mention all the forms of calculus, string theory, Quantum entanglement, quantum mechanics\physics, etc and etc.

A lot of fundamental maths is turning out to be anticipated in the Bible. John Elias wrote a book, Proof of God, about it and I recommend you take a look. It's on Amazon. You might also like to take a look at my academia article Genesis 1.1: A Numerical Cypher.https://www.academia.edu/164828704/Gene ... cal_Cypher

KingJamesMath wrote: Sun Mar 15, 2026 6:37 am
106 + 560 + 000 = 666

The number 2701 occupies 165 + 166 + 167 + 168 = 666

366+388+231+38 = 973.png


In the KJV the name Jesus occurs 973 times.

That's an unusual technique, adding the digits in groups of three or from related sources. I'm not saying it's wrong and I've seen others do it, but I've never tried it. Have you found it useful?

bluetriangle wrote: Sun Mar 15, 2026 3:57 am 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.

Brother Bill! I believe you are correct. It does seem like God inspired me to post the Conway Circle Theorem so He could then inspire you to do your beautiful analysis. As it turns out, the ratios you found are true for any equilateral triangle and only for an equilateral triangle.

To use standard mathematical terms, the "outer circle" is called the circumcircle. It's center is called the circumcenter. Here's a wiki article that defines them.

The circumcenter and the incenter coincide ONLY in an equilateral triangle.

Likewise, the integer ratios 28 and 7 are found ONLY if the triangle generating the Conway Circle is equilateral.

You've really found an amazing little gem here Bill! The ratios that yield 28 and 7 are intrinsic to all equilateral triangles.

I'm gonna dig in more and report back.

Peace,

Richard

KingJamesMath wrote: Sun Mar 15, 2026 7:59 am Proverbs 8:27
When he prepared the heavens, I was there: when he set a compass upon the face of the depth:


I was there שם אני (Hebrew Text) = 401

the Word Jesus the Aleph and Tav (1 + 400) = 401

That a beautiful find.

We find the same phrase expressing the same idea of God "being there" from the beginning in this verses:

Isa 48:16 Come ye near unto me, hear ye this; I have not spoken in secret from the beginning; from the time that it was, there am I: and now the Lord GOD, and his Spirit, hath sent me.

What a beautiful verse! Nothing compares to knowing the Eternal God who reveals Himself to us through His Word and His Spirit! I am there.

KingJamesMath wrote: Sun Mar 15, 2026 7:59 am Rom 8:39 Nor height, nor depth, nor any other creature, shall be able to separate us from the love of God, which is in Christ Jesus our Lord.

the love της αγαπης (Greek) 801

the Word Jesus the Alpha and Omega (1 + 800) = 801

The Number 801 = Alpha Omega = The Creator = Dove

https://www.biblewheel.com/GR/GR_801.php

KingJamesMath wrote: Sun Mar 15, 2026 7:59 am Gen 1:2 And the earth was without form, and void; and darkness was upon the face of the deep.
And the Spirit of God moved upon the face of the waters.

the Spirit of God רוח אלהים (Gematria Value) 300
of the earth 300x

Yes, The Spirit of God = 300 = Shin (21st letter) and Shin represents fire. See https://www.biblewheel.com/GR/GR_300.php

And the number 300 returns us to Proverbs 8:

Pro 8:19 My fruit (פִּרְיִי = 300) is better than gold, yea, than fine gold; and my revenue than choice silver.