I noticed something recently about polygonal numbers and their relationship to the number 9 that I wanted to share ...
The highest single digit in the sequence of positive integers = 9 and the number 9 represents pregnancy or birth (corresponding with the 9 months of pregnancy).
ALL polygonal numbers have an infinitely repeating digital root cycle of *9* digits that ALWAYS begins with 1 and ends with *9*. Here are the digital root cycles for the first *9* polygons ...
Triangular numbers = 1, 3, 6, 1, 6, 3, 1, 9 and 9.
Square numbers = 1, 4, 9, 7, 7, 9, 4, 1 and 9.
Pentagonal numbers = 1, 5, 3, 4, 8, 6, 7, 2 and 9.
Hexagonal numbers = 1, 6, 6, 1, 9, 3, 1, 3 and 9.
Heptagonal numbers = 1, 7, 9, 7, 1, 9, 4, 4 and 9.
Octagonal numbers = 1, 8, 3, 4, 2, 6, 7, 5 and 9.
Nonagonal numbers = 1, 9, 6, 1, 3, 3, 1, 6 and 9.
Decagonal numbers = 1, 1, 9, 7, 4, 9, 4, 7 and 9.
Hendecagonal numbers = 1, 2, 3, 4, 5, 6, 7, 8 and 9.
EVERY successive set of *9* polygons produces THE EXACT SAME REPETITION CYCLES of the first *9* polygons (to infinity). For example, look at the digital root cycles for the very next set of *9* polygons ...
12-gonal numbers = 1, 3, 6, 1, 6, 3, 1, 9 and 9.
13-gonal numbers = 1, 4, 9, 7, 7, 9, 4, 1 and 9.
14-gonal numbers = 1, 5, 3, 4, 8, 6, 7, 2 and 9.
15-gonal numbers = 1, 6, 6, 1, 9, 3, 1, 3 and 9.
16-gonal numbers = 1, 7, 9, 7, 1, 9, 4, 4 and 9.
17-gonal numbers = 1, 8, 3, 4, 2, 6, 7, 5 and 9.
18-gonal numbers = 1, 9, 6, 1, 3, 3, 1, 6 and 9.
19-gonal numbers = 1, 1, 9, 7, 4, 9, 4, 7 and 9.
20-gonal numbers = 1, 2, 3, 4, 5, 6, 7, 8 and 9.
And notice that the *9th* polygons in EACH successive series of *9* polygons are the ONLY ones with digital root cycles consisting of the digits 1 through *9* in SEQUENTIAL ORDER.
When we place the infinitely repeating digital root cycles of every successive set of *9* polygons on a 9 x 9 table, we see that the sum of EACH of the *9* columns has a digital root of *9*.
The TOTAL SUM of the infinitely repeating digital root cycles of every successive set of *9* polygons = The PRODUCT of *9* and the sum of the first *9* positive integers (45).
Hence, *ALL* polygonal numbers (to infinity) are related to the number *9* (through their digital roots). This shows we can find HIDDEN features in the families of numbers by breaking them down to their digital roots.
I am Gambini and I assure you that all potential polygonal shapes have their origin in the WOMB of creation
Last edited by Gambini; 08-24-2014 at 06:35 PM.
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Does that comment have any content? Are you saying that numbers that don't fit that pattern do NOT "have their origin in the WOMB of creation"?
For example, the star numbers, which include the prime factors of Genesis 1:1 = 2701 = 37 x 73, do not fit the pattern. The digital roots of those numbers follow the repeating pattern of 1, 4, 1, 4, 1, 4 .... Does that mean they do not have their "have their origin in the WOMB of creation"?
- Skepticism is the antiseptic of the mind.
- Remember why we debate. We have nothing to lose but the errors we hold. Who but a stubborn fool would hold to errors once they have been exposed?
Check out my blog site
I'm saying ALL of the *regular* polygons are related to the number *9* (through their digital root cycles), which symbolizes pregnancy. So metaphorically speaking, the highest single digit is "pregnant" with ALL the *regular* polygonal shapes (to infinity). And the infinite series of polygonal shapes represents creation (hence, the womb of creation).
Originally Posted by Richard Amiel McGough
Actually the Hexagram series is 1, 4, 1, 1, 4, 1 ... That is, the digital root cycle = 1,4 and 1. Hexagrams are an extension of Hexagons. So in that sense, they DO go back to the number *9*. Regardless, I'm strictly dealing with the *regular* polygons.
Hey, have you ever noticed this ...
If we make a top to bottom list of the infinite series of polygonal numbers (with rows and columns), we find that starting with the first SQUARE and moving diagonally, we get the unbroken sequential series (in perfect order) of the CONSTANTS in every successive magic square (to infinity).
BINI aka The Mystic Meanie
Last edited by Gambini; 08-28-2014 at 12:55 PM.
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