Lift up your eyes on high, and behold who hath created these things, that bringeth out their host by number: he calleth them all by names by the greatness of his might, for that he is strong in power; not one faileth.

Isaiah 40:26

Figurate Numbers are numbers that can be represented as a regular array of points, such as a triangle, square, or pentagon. Such numbers figure prominently in Scripture and are a highly significant part of its divine design. I am greatly indebted to Vernon Jenkins for his pioneering work in this area. His introduction  to this topic and its relation to Scripture is well worth reading. Another excellent introduction - from a purely mathematical point of view - may be found in the Figurate Number  article on MathWorld  site.

Many of the significant numbers found in Scripture are members of geometric number sequences. For example, the entire Canon is divided into segments that contain 5, 12, or 22 Books. As discussed below, these three numbers of the second, third, and fourth terms of the Pentagonal Number Sequence. An excellent site that has a huge searchable database of such number sequences is found at The On-Line Encyclopedia of Integer Sequences 

Triangular Numbers:

The n^th Triangular Number is the sum of all the numbers from 1 to n. It is represented as T(n). For example, the number of fish caught in John 21 is the seventeenth triangular number:

T(17) = 1 + 2 + ... + 16 + 17 = 153

This relation has been known and meditated upon since at least the 5th century when Augustine commented on it in his his Tractate 122  on John 20:30-21:11.

Notation Change: When I first designed this website, I denoted triangular numbers with the heuristic "Sum(n)" to remind the non-mathematically trained reader that the nth triangular number is formed by summing the integers from 1 to n. But I have since come to realize that every extra symbol clutters the equations, and so have decided to change the notation to the simpler and standard "T(n)." Readers therefore may encounter triangular numbers represented either as T(n) or Sum(n) until I have completed the update.

Triangular Numbers appear frequently in Scripure. Here are a few of the more obvious, with their associated concepts:

Index	Value	Associated Concepts
1	T(1) = 1	All geometric numbers begin with the value "1" which is therefore called the "trivial case."
2	T(2) = 3	The Trinity: The Spirit (3) proceeds from the Father (1) and the Son (2). This manifests with great clarity on Spoke 3 as discussed on pages 164-5 of the Bible Wheel book, reproduced online here.
3	T(3) = 6	Creation of Man and Cosmos: Six = 600 = Cosmos. Six is a "perfect number" in that 1 + 2 + 3 = 1 x 2 x 3 = 6. It is profoundly integrated with the Creation Holograph as well as Spoke 6 of the Bible Wheel.
4	T(4) = 10	Number of the Ten Commandments and base of the Bibical numerical system. It is profoundly integrated with Spoke 10 of the Bible Wheel.
7	T(7) = 28	The Number of words (7) and letters (28) of the Creation Holograph (Genesis 1.1) which sums to 2701 = T(73)! [See below]
11	T(11) = 66	The Number of Books in the Wheel, and the value of the word Wheel itself: Wheel Galgal = 66
19	T(19) = 190	The Index and the Value are related through this fundamental identity from Genesis 3: Rib Tsalo = 190 = T(19) = T(Eve)
23	T(23) = 276	The Number of souls saved in Paul's shipwreck (Acts 27.37)
24	T(24) = 300	The Value of (Ruach Elohim, The Spirit of God). This is an extremely profound relationship.
32	T(32) = 528	The KEY to the Bible = T(32)! (Note: The Hebrew for Heart is Lev = 32)
36	T(36) = 666	The Number of the Beast (Rev. 13.18).
43	T(43) = 946	The Spirit = T(43) (Note: The Hebrew word for "Greatness" is Gadol = 43. This is the primary role of Holy Spirit - to magnify the Father and the Son.
73	T(73) = 2701	The sum of Genesis 1.1, the Creation Holograph. It is expressible as a very simple combinations of elements from the Holographic Generating Set: 2701 = BC = T(C) = T(B) + AB
112	T(112) = 6328	The sum of Genesis 1.1 + John 1:1 from the Creation HyperHolograph. The index 112 = YHVH Elohim (The LORD GOD) from the Unity Holograph (Shema). It also is expressible as a simple combination of the Holographic Generating Set: 6328 = AB + C2

Square Numbers:

Square Numbers are associated with structure - e.g. the Altar, The Temple, and the New Jerusalem are all described as foursquare, as was the camp that formed a Cross in the Wilderness. This is particularly astouding in light of this pair of identities:

We also have the identity:

The Kingdom of God is ruled by Truth, which is a Square Number in both Hebrew and Greek:

This manifests in popular numerical slang that takes "foursquare" as representing Truth, Honesty, and Integrity.

Another significant Square is found in the Number 144, which represents the Elect of God and eternal citizens of the New Jerusalem:

This is tremendously significant, in that the pattern based on the Number 12 was established in the Hebrew Testament, yet it manifests in the intrinsic alphanumeric structure of the Greek language and the explicit message of the text of the New Testatment (Revelation 14.1)!