Gambini

08-24-2014, 06:23 PM

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 :pray:

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 :pray: