THE UNIQUE NUMERICAL HEXAGON, 1801
A numerical hexagon, order n, is the derivative, by symmetrical self-intersection, of a numerical triangle of order (3n-2)*.
Here are some relevant facts concerning a numerical hexagon, order n:
S (number of counters forming a side) = n
R (number of rows of counters) = 2n-1
O (number of counters forming its outline) = 6(n-1)
A particularly interesting situation arises when n = 25, for then, S = 25, R = 49 and O = 144 - all squares! The triangle which generates this unique result is the 73rd, i.e. 2701 - the characteristic value of Genesis 1:1 (representing the first 7 Hebrew words of the Judeo-Christian Scriptures). Here is a view of this construction:
*Such triangles are built around a single central counter, and because of their ability to generate hexagons (by self-intersection) and hexagrams (by self-union) they are designated G-triangles.
Vernon Jenkins MSc
2007-05-06