There is a simple whole number (integer) matrix grid table upon — and within — that every possible whole number Pythagorean Triangle — a.k.a. Pythagorean Triple — can be placed, and proved. The Brooks Base Square  Inverse Square Law (BBSISL) matrix is an infinitely expandable grid that reveals ALL Pythagorean Triples — both Primitive Triples (PPT) and their nonPrimitive multiples (nPTT). An extremely simple geometric AREA proof of the Pythagorean Theorem — c2=a2+b2 — is built into the BBSISL matrix.
Not only does the Inverse Square Law describe, define and quantify our most important energies (and their expressions as force)— gravity, light, sound, electromagnetism... — the BBSISL matrix grid is composed of Pythagorean Triples crisscrossing over much of the entire grid. An intimate interconnection way beyond a simple, casual association has been revealed. The Dickson Method confirms, validates and provides insight into the generation of ALL Pythagorean Triples. Please see the TPISC project white paper for the full mother load.
Full Description
There are two parts to TPISC: The Pythagorean — Inverse Square Connection ~A MathspeedST Supplement~:
 INTRO to TPISC (This Overview)
 TPISC (white paper)
In this INTRO to TPISC, you get a greatly simplified introduction and overview of TPISC: The Pythagorean — Inverse Square Connection white paper.
The actual white paper (TPISC) is packed full of visual media, charts and tables to follow the process of discovery. The relationships — connections and interconnections — between the BBSISL matrix and the Pythagorean Theorem (as Pythagorean Triples) is so vast that the process of simplifying it down to consistent, irrefutable and concrete visuals became the motivation and driving force of this entire project.
What is so amazing about the BBSISL matrix?
If you scan each Row/Column, only some have squared numbers. If they do, the squared numbers always come in pairsets. In every case, those square number pairsets are the AREAS of the two shorter sides ("a" and "b") of a Pythagorean Triple triangle. The longer hypotenuse (c) AREA is located on the Prime Diagonal — the diagonal line dividing the matrix grid evenly into two symmetrical halves!
This is their story.
Work metadata
 Year Created: 2014
 Submitted to ArtBase: Monday Aug 18th, 2014
 Original Url: http://www.brooksdesignps.net/Reginald_Brooks/Code/Html/MSST/TPISC/BBS_Pythag_netart17/BBS_Pythag_netart17.html

Work Credits:
 reginaldbrooks, primary creator
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Artist Statement
Right next to Einstein's E=mc2, and, the diminishing influence with distance relationship know as the Inverse Square Law (ISL), the Pythagorean Theorem — c2=a2+b2 — is probably one of the most well known mathematical statements. (Not counting simple formulas.)
It certainly is one of the oldest. Thousands of years ago, a string with knots at 3 units, followed by 4 more units, followed by 5 more units, when closed up, was found to form a perfect 345 rightangle triangle. Game on!
While Pythagorean Triangles can be formed with both whole and fractional numbers, it is with whole number integers (1,2,3...) — like in the 345 triangle — that they shine light on their relationships to other geometric forms and subsequent mathematical ideas!
Pythagorean Triangles that are composed solely of whole number integers are called Pythagorean Triples (PTs).
Some PTs — like the 345 — are as reduced and simple as they can get. Others are multiples of the simple primitive PTs. For centuries now, efforts have been made to identify ALL of them — primitives and nonprimitives (multiples), alike. Along the way, thousands of proofs of the Pythagorean Theorem have issued forth.
In July of 2014, TPISC: The Pythagorean — Inverse Square Connection ~A MathspeedST Supplement~ — was introduced. ALL Pythagorean Triples and their proofs are directly visible right on — within, really — that symmetrical, expanding grid of whole numbers describing the Inverse Square Law: The BBSISL matrix.
TPISC is a natural, builtin relationship within the very foundational core of the BBSISL matrix. Come see for yourself!