*Statement*

Introducing *TPISC I: Basics*, an ebook.
*TPISC* is a supplement to *MathspeedST* (published in November, 2013).

While *LightspeedST* addressed the ultimate question: “Why is the speed of light constant?”*MathspeedST* addressed the fundamental, underlying question: “How can information be ubiquitous, effectively traveling FASTER than the speed of light?”

*TPISC* describes the Pythagorean Triangles (Triples) and their ubiquitous connection to the unfolding **Inverse Square Law (ISL)** as depicted in the **BBS-ISL Matrix**.

The **BBS-ISL Matrix (Brooks Base Square Matrix)** presents the **ISL** as a natural, whole integer number matrix grid that expands to infnity.

*TPISC* is also, by definition, grounded in natural, whole integer numbers forming the sides of the Pythagorean Triples (PT). The PTs also expand to infinity and are deeply embedded within the **BBS-ISL Matrix** throughout their co-expansion. Enter *TPISC*.

*TPISC I: Basics* provides the simple, introductory geometrical (Visual) and algebraic (Calculation) mathematical basis for the accounting and distribution of all Pythagorean Triple Triangles — primitive and non-primitive — directly on the **BBS-ISL Matrix**.

This freely available interactive ebook brings together under one publication the intersection of two geometries: The Pythagorean Triangles and the **BBS-ISL Matrix** under the title *TPISC I: Basics*. It includes hundreds of images, a number of videos and lots of test-yourself, interactive widgets in presenting the layout, proofs, and patterns of the Pythagorean Triples and their **ISL**-derivation and, ultimately, the mathematical basis of their connection with the matrix. Ages 13 and up, or younger if you are up to the task. Basically, if you can add and subtract, meaning you can multiply and divide, you can easily gain access to *TPISC*. Both *TPISC* and the **BBS-ISL Matrix** are composed solely of natural, whole integer numbers. No decimals, fractions, integrals, differentials,.... Nothing you can't handle! But plenty in the Advanced form to keep you going for...(ever!).

A new paradigm in the visualization of basic mathematics is presented!

*Description:*

*TPISC I: Basics*
*TPISC I: The Pythagorean - Inverse Square Connection: Basics* reveals the presence, proofs and and overall distribution of the Pythagorean Triples (PTs) upon the **BBS-ISL Matrix**. The distribution was shown as occurring on, and only on, each and every Row/Column that contained AREA Squares. Scan the Rows and if they contained Pair-Sets of these AREA Squares you would always find a PT there.

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Abstract

There is a simple whole number (integer) matrix grid table that every possible whole number Pythagorean Triangle — a.k.a. Pythagorean Triple — can be found and proved. The **Brooks Base Square - Inverse Square Law (BBS-ISL) Matrix** is an infinitely expandable grid that reveals ALL Pythagorean Triples — both Primitive Triples (PPT) and their non-Primitive multiples (nPTT). An extremely simple geometric AREA proof of the Pythagorean Theorem — c2=a2+b2 — is built into the** BBS-ISL 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 **BBS-ISL Matrix** grid is composed of Pythagorean Triples crisscrossing over much of the entire grid. An intimate inter-connection way beyond a simple, casual association has been revealed. The *Dickson Method* confirms, validates and provides insight into the generation of ALL Pythagorean Triples.

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Introduction

The reason that this work is being presented is precisely because the very nature of that geometric relationship of the Pythagorean Triangle (PT) — whereby the AREA of the square of the long side (hypotenuse) is equal to the sum of the Squares of the two shorter SIDES (legs) — is so intimately related to the **Inverse Square Law (ISL)**, as depicted in the **BBS-ISL Matrix**, that a cause and effect relationship between the two is unavoidable.

That the **BBS-ISL Matrix** provides the simplest, most intuitively obvious proof to the Theorem directly on the grid only supports the argument. Every possible PT, and its proof, is visually and mathematical present. The *Dickson Method* confirms this.

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Conclusion

More than adequately covered in the literature, writings, songs and art of all cultures, it has been an attempt here to present an entirely new manner of looking at the Pythagorean Triples, their proofs, distribution and ultimately their inter-connections. As it turns out, the inter-connections with the **BBS-ISL Matrix** are what has become the main theme. As the **Inverse Square Law (ISL)** upon which the **BBS-ISL Matrix** is formed is, in many respects, one of, if not the main, “laws” or relationship informing principles in all of science — most especially physics and mathematics. That the PT should be so intimately born, described and proved within that matrix is not without great introspection. If the **ISL** is fundamentally about how influence is distributed — spread out and diluted — over SpaceTime (ST), then the Pythagorean Theorem is a natural, built-in measure of that.

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Table of Contents

1. Introduction
2. TPISC—BBS-ISL (Visualizations)
3. Dickson Method (Calculations)
4. Inter-Connections
5. TPISC II: Advanced (preview 1)
6. Summary
7. Conclusion
8. Links & References
9. Appendix
10. Next—TPISC Advanced (preview 2)
11. Review
12. Next: BBS - ADVANCED (preview)
13.

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*TPISC II: Advanced*

*TPISC II: The Pythagorean - Inverse Square Connection: Advanced* — a separate ebook — profoundly enlarges upon the *Dickson Method* — giving the *Extended Dickson Method* — which has opened the doors to the real connection between the **ISL** and the PTs. Patterns of Fractal-like Relationships, is a descriptive phrase loaded with the implications that the PTs, while ubiquitously embedded throughout the infinite **BBS-ISL Matrix**, grow within it in a profoundly fractal-like pattern. Parsing these into *r-set* and *s-set* groups becomes key in determining the pattern distribution of ALL PTs.

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Platforms

This is a multi-touch, interactive ebook made with iBooks Author and published in the Apple iBooks Store. Currently, it requires an iOS or MAC device and the free iBooks app, to download and read..

*Multi-touch, interactive eBook*: TPISC_I: Basics ebook

*Selected SCREENSHOTS for TPISC I: Basics*

*This ebook is freely available in the iBooks Store download link above (No Auto-downloads---just info).*

(NOTE: iBooks are available for reading on your Mac or iOS device.)

Artist Link in iTunes iBooks Store: Reginald Brooks

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LINKS

TPISC I: Basics The Pythagorean — Inverse Square Connection ©2015, Reginald Brooks, Brooks Design. All rights reserved.

click HOME to return to the home page.

TPISC II: Advanced The Pythagorean — Inverse Square Connection ©2015, Reginald Brooks, Brooks Design. All rights reserved.

click HOME to return to the home page.

TPISC III: Clarity Tree of Primitive Pythagorean Triples (ToPPT) ©2017, Reginald Brooks, Brooks Design. All rights reserved.

click HOME to return to the home page.

MathspeedST: Leapfrogging LightspeedST FASTER than The Speed of Light ©2013, Reginald Brooks, Brooks Design. All rights reserved.

click HOME to return to the home page.

LightspeedST: Leapfrogging @ The Speed of Light ©2013, Reginald Brooks, Brooks Design. All rights reserved.

click HOME to go to the LightspeedST ebook home page.

~ MathspeedST: The Ubiquitous Information of Numbers white paper~ LightspeedST: Leapfrogging @ The Speed of Light

T H E U B I Q U I T O U S I N F O R M A T I O N O F N U M B E R S new media net.art project

~ MathspeedST: Leapfrogging Lightspeed FASTER than The Speed of Light MOVIES

The contents of TPISC I: Basics, and both MathspeedST and LightspeedST, can be viewed as White Papers in the Art Theory 101 links below.

**Relevant White Papers by the Author**

**http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/arthry5.htm**

**titles and topics:**

**Page 5a:****Dark-Dark-Light: Dark Matter = Dark Energy (the inverse of) .****Page 5c:****The History of the Universe - update- "The Big Void" .****Page 6:****The LUFE Matrix.****Page 7:****The LUFE Matrix Supplement.****Page 9:****The LUFE Matrix: E=mc2****Page10:****Quantum Gravity..by the book****Page11:****Conservation of SpaceTime****Pages 12a-p: digitized version of the original 1985 L.U.F.E. manuscript****Page 12a:****LUFE: The Layman's Unified Field Expose`**

~Introduction-Contents-List of Figures~**Pages 15-19:****MathspeedST****Page 16:****Brooks (Base) Square interactive (BBSi) matrix: Part I: BASICS****Page 18:****Numbers Of Inevitability ~ Let's do a number on that!****Page 19:****AFPOP: A Fresh Piece of Pi(e)...and the √2, too...Fractal - Fractal - Fractal****Pages 20-27:****LightspeedST****Page 20:****LightspeedST: 1. 20 Questions****Page 21:****LightspeedST: 2. 20 Answers****Page 22:****LightspeedST: 3. Mechanics of ST****Page 23:****LightspeedST: 4. The Movie Script****Page 24:****LightspeedST: 5. The Movie****Page 25:****LightspeedST: 6. Links + References****Page 26:****LightspeedST: 7. Quark Portraits****Page 27:****LightspeedST: 8. Triad~ruminations****Page 28:****LightspeedST: the eBook (complementary to MathspeedST)**

**Page 29:****MathspeedST: the eBook (complementary to LightspeedST)****Page 30:****MathspeedST_The Ubiquitous Information of Numbers (complementary to LightspeedST)****Page 31:****TPISC: The Pythagorean — Inverse Square Connection: A MathspeedST Supplement****Page 32:****TPISC: INTRO to The Pythagorean — Inverse Square Connection: A MathspeedST Supplement****Page 37:****Time and Structure ~ with BBS-ISL Matrix, ISL, and TPISC****Page 40:****BIMtree-ToPPT_AREAS: 12 Easy Pieces****Page 43b:****TPISC_IV_Details: BIM + PT + DNA + Epstein-Barr Virus****Page 44:****TPISC_IV_Details: BIM + PT + Decagon (double Pentagons)****Page 45:****TPISC_IV_Details: Phi, Fibonacci, Pentagon Connections to the PTs****Page 46:****TPISC_IV_Details: BIM + Primitive Pythagorean Triples + the PRIMES****Page 47:****TPISC_IV_Details: DSEQEC (Double-Slit Experiment – Quantum Entanglement Conjecture, Part I of II)****Page 49:****TPISC_IV_Details: CaCoST — Creation and Conservation of SpaceTime (Part II of II)****Page 50:****TPISC_IV_Details: BIM: How to Make (with Spreadsheet App)****Page 51:****Big OUTLINE for TPISC IV: Details****Page 53:****TPISC_IV_Details: Simple Path from the BIM to the PRIMES****Page 54:****TPISC Artworks****Page 55:****PRIMES vs NO-PRIMES ebook**

KEYWORDS TAGS: TPISC, The Pythagorean - Inverse Square Connections, Pythagorean Triangles, Pythagorean Triples, primitive Pythagorean Triples, non-primitive Pythagorean Triples, Pythagorean Theorem, Pythagorus Theorem, The Dickson Method, BBS-ISL Matrix, Expanded Dickson Method, r-sets, s-set, t-sets, Pair-sets, geometric proofs, MathspeedST, leapfrogging LightspeedST FASTER than the speed of light, Brooks (Base) Square- Inverse Square Law (ISL), BBS-ISL matrix grid, The Architecture Of SpaceTime (TAOST), The Conspicuous Absence Of Primes (TCAOP), A Fresh Piece Of Pi(e), AFPOP, Numbers of Inevitability,LightspeedST, Teachers, Educators and Students (TES), number theory, ubiquitous information, FASTER than the speed of light, primes, prime numbers, fractals, mathematics, Universe, cosmos, patterns in number.

Art Theory 101 / White Papers Index