## Equation for Converting Numbers into Geometric Solids?

Discussions concerned with knowledge of measurement, properties, and relations quantities, theoretical or applied.  ### Equation for Converting Numbers into Geometric Solids?

In the Pythagorean understanding of number, all numbers have a corresponding geometric value. Each number corresponds to a set of points, with the points themselves connected through lines. These lines, in themselves must also be numbers. The problem occurs as to how one converts a number in a geometric structure, when the number itself as points, must contain a separate number as lines that must connect to each corresponding point in order to exist as a geometric form. In simpler terms each point of x number must connect to each point that composes x number, which each point synonymous to value of 1.

The following observes this problem:

2 points requires 1 line
3 points requires 3 lines
4 points requires 6 lines
5 points requires 10 lines
6 points requires 15 lines
7 points requires 21 lines
8 points requires 28 lines
9 points requires 36 lines

We can observe further that each set of lines differs by an numerically ascending value of 1

1 and 3 differ by 2
3 and 6 differ by 3
6 and 10 differ by 4
10 and 15 differ by 5
15 and 21 differ by 6
21 and 28 differ by 7
28 and 36 differ by 8

So we see a dual numerical sequence that corresponds with the original one composed of points.

The question occurs as to calculate each numbers inherent connections, or the connects which in themselves approximate the points. This approximate, as the observation of a connection delves somewhat in chaos theory in these regards.

In these respects the equation (α-1) * α(1/2) = ε → {α,ε} appears to provide the solution where "α" equal the number as point and "ε" equals the corresponding lines which approximate the points. In these respects, from a geometric perspective all numbers are conducive to sets in themselves.

Thoughts?
Eodnhoj7
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Posts: 102
Joined: 02 Mar 2018    ### Re: Equation for Converting Numbers into Geometric Solids?

Eodnhoj7 » May 26th, 2018, 10:54 am wrote:
We can observe further that each set of lines differs by an numerically ascending value of 1

1 and 3 differ by 2
3 and 6 differ by 3
6 and 10 differ by 4
10 and 15 differ by 5
15 and 21 differ by 6
21 and 28 differ by 7
28 and 36 differ by 8

Thoughts?

This is because each added point simply adds lines to that point from each of the points already included. mitchellmckain
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Posts: 1300
Joined: 27 Oct 2016    ### Re: Equation for Converting Numbers into Geometric Solids?

mitchellmckain » May 26th, 2018, 1:16 pm wrote:
Eodnhoj7 » May 26th, 2018, 10:54 am wrote:
We can observe further that each set of lines differs by an numerically ascending value of 1

1 and 3 differ by 2
3 and 6 differ by 3
6 and 10 differ by 4
10 and 15 differ by 5
15 and 21 differ by 6
21 and 28 differ by 7
28 and 36 differ by 8

Thoughts?

This is because each added point simply adds lines to that point from each of the points already included.

Yeah I know, but that is the origin of all geometric structures: A point extended from a point through a line. It observes each point is connected to another point, with these multiple points acting as the field with the line being the "localization" as a form of connection through relation.

All points exist through a point with the multiplicity of points observing an approximation of a unified point by observe their connection as "relations" of these multiple points. Mulitplicity is an approximation of unity and all geometric forms extend from 1 point in space.

I am arguing, or maybe should have elaborated further on, the fact that all relations of points inherently result in geometric objectis and if we look at geometry quantiatively (not qualitatively) a specific group of points always results with a corresponding set of geometric objects.

3 points, with three lines always connecting them always results in a approximate of a triangel.

4 points a square along with relative triangles (an maybe trapezoids if I look at it again)

etc.

All points as extensions of eachother are inherently connected as "point through points" hence the connection t
Eodnhoj7
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