*Statement*

Introducing *TPISC III: Clarity & Simplification: Tree of Primitive Pythagorean Triples (ToPPT)*, an ebook.
*TPISC III:* is the third 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?”

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

1 banana, 2 banana, 3 banana, 4 … and there’s so much more!

A simple curiosity on how even simpler Whole Integer Numbers (WINs), when squared, form a law that rules the Universe — indeed, SpaceTime (ST) itself — has been a source of awe and wonder for quite some time. This is the **Inverse Square Law (ISL)**.

The “inverse” means it’s per area. When the WINs are squared, you get the area.

The forms and forces of Nature obey the **ISL**. The initial concentration of an impulse or influence of energy dissipates in a known manner as it expands out from its source. A wonderful and ubiquitous law in forming the ST that builds the Universe. And it doesn’t even need to travel to get there…it is known!

Now, on top of this beautiful law and all the magnificent forms and expressions it can offer, comes yet another sublimely beautiful law — or theorem — that also relates areas to significant form — the Pythagorean Theorem: the long, hypotenuse side squared = the sum of the two squared shorter sides of a 90°-right triangle.

When these triangles are made solely of WINs, we have Pythagorean Triples (PTs).

The PTs are a major subset of the **ISL** and as such are both infinite in number and ubiquitous in distribution along with the **ISL**. Their structural beauty lies in the fractal-nodes of slight asymmetry they give to the expanding expression of the **ISL**. They give new forms!

Not only can these PT fractals be located throughout the **BBS-ISL Matrix**, together they form a linked structure relating all the parts to the whole, in the form the * Tree of Primitive Pythagorean Triples (ToPPT)*.

This clarity and simplification of form has become the focus of this work. The non-isosceles right triangles, rectangles and ovals of the

3 potato, 4 potato, 5 potato squared …

“

The

Excerpt From: Reginald Brooks. “TPISC_III-Clarity...” iBooks.

Platforms: This is a multi-touch, interactive ebook made with iBooks Author and published in the Apple iBookstore. Currently, it requires an iPad, or OS X running on a Mac, and the free iBooks app to download and read.

Most of the same content is found online here on my website in the form of white papers and multi-media. HERE is the Media Center link.

*Selected SCREENSHOTS for TPISC III: Clarity*

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

Artist Link in iTunes iBookstore: Reginald Brooks

~---

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

**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**

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