TPISC III: Clarity & Simplification: Tree of Primitive Pythagorean Triples (ToPPT) ~A MathspeedST Supplement~
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 ToPPT join with the isosceles right triangles, squares and circles of the ISL to generate our ST Universe — giving expression to the Universal mathematical constructs.
3 potato, 4 potato, 5 potato squared …
“BIM — BBS-ISL Matrix — is the geometry defining SpaceTime!”
MathspeedST: Leapfrogging Lightspeed FASTER than The Speed of Light
The MathspeedST Supplements:
• TPISC I: Basics
• TPISC II: Advanced
• TPISC III: Clarity & Simplification (ToPPT)
• TPISC IV: Details (coming)
• TPISC V: Exponentials (coming)
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
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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 MathspeedST and LightspeedST, as well as most of the TPISC Series, 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.