*Statement*

Introducing *TPISC II: Advanced*, 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* provided 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**.

*TPISC II: Advanced* greatly expands upon the simple, introductory geometrical (Visual) and algebraic (Calculation) mathematical basis presented in *TPISC I: Basics*. By further development of the *Dickson Method* (DM), the *Expanded Dickson Method* (EDM) is fully presented. Parsing the *r-sets*, and the *s-sets* and *t-sets* that result, onto the **BBS-ISL Matrix** reveals profound connections between the basic layout of the matrix and the distribution of the Pythagorean Triples. A complete geometric visualization is realized and this leads ultimately to the *r-set Flow Chart* that simplifies the entire distribution of ALL Pythagorean Triples — primitive and non-primitive PTs.

This interactive ebook brings together under one publication the intersection of two geometries: The Pythagorean Triangles and the **BBS-ISL Matrix** under the title *TPISC II: Advanced*. 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!). *TPISC I: Basics* (free) is definitely the place for most to start.

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

*Description:*

*The Pythagorean - Inverse Square Law Connection* — or how the Pythagorean Theorem is intimately embedded within the *The Architecture Of SpaceTime (TAOST)* as described by the **BBS-ISL Matrix** — is first and foremost the topic of this book.

This work is being presented precisely because the very nature of that geometric relationship of the Pythagorean Triangle (PT) is so intimately related to the **Inverse Square Law (ISL)**, as depicted on the **BBS-ISL Matrix**, that a cause and effect relationship between the two is unavoidable

That the **BBS-ISL Matrix** also 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.

*TPISC I: Basics*

*TPISC I: The Pythagorean - Inverse Square Connection: Basics* — a separate ebook — revealed 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.

*TPISC II: Advanced*

*TPISC II: The Pythagorean - Inverse Square Connection: Advanced* 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.

Every grid cell # within the **BBS-ISL Matrix** is determined by the Prime Diagonal #s, as is every possible PT.

The PTs, just like the circle and square, define the **ISL**!

So in the end, what are we to make of all this?

Why the **BBS-ISL Matrix** — which begs the question: Why the **Inverse Square Law (ISL)** — and why the
Pythagorean Triples?

And so what if they are both made up of whole integer #s?

And so what if they both expand to infinity?

And so what if the the PTs seem to be all inter-connected?

And so what if the Pts seem to be infinitely embedded within the **BBS-ISL Matrix**?

And so what if there is a pattern to how they are embedded?

And so what if they both share a common pattern of 90° right-angle isosceles triangle relationships?

And so what if the **ISL** informs all of SpaceTime?

And so what if the **ISL** thus informs all expressions of energy as matter & waves — particles & fields?

And so what if all such interactions — including those of growth — is predicated on the unfolding of the **ISL**-dependent SpaceTime?

And so what if those simple PTs — pattern- peppered throughout the **BBS-ISL Matrix** — are laying down networking nodes of optimal 90° right-angle connections amongst the more widely distributed **ISL** background structure?

Are not the PTs there to organize it all?

*TPISC, The Pythagorean — Inverse Square Connection* , is about shining some light on how Nature ubiquitously builds combining simple, elemental forms into sentient constructs able to reflect the light all the way back home!

Table of Contents:

1. Introduction
2. The Underlying Question
3. TAOST (The Architecture Of SpaceTime)
4. TCAOP(The Complete Absence Of Primes)
5. Interconnectedness
6. Conclusion
7. Links & References
8. Appendix
9. Dyamic Interactive BBS-ISL matrix
10. Numbers of Inevitability
11. AFPOP: A Fresh Piece Of Pi(e)...and the Square Root of 2, too.
12. Next: BBS - ADVANCED (preview)
13. Review

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 Mavericks running on a Mac, and the free iBooks app to download and read.

*Multi-touch, interactive eBook*: TPISC II: Advanced ~ eBook

*Selected SCREENSHOTS for TPISC II: Advanced*

(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****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