TPISC IV: Details, DSEQEC and PRIMES eBook

~A MathspeedST Supplement~


*TPISC ( pisque—silent “T”): *The Pythagorean — Inverse Square Connection


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). BIM (BBS-ISL Matrix) is the matrix grid that mathematically describes the ubiquitous nature of the 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 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.


TPISC IV contains all of the above plus:

  • PTOP (Periodic Table Of PRIMES) & the Goldbach Conjecture;
  • PRIMES On the BIM, and;
  • *DESQEC & CaCoST;
  • as well as “details” of the earlier TPISC I-III works.

*DSEQEC (Double-Slit Experiment—Quantum Entanglement Conjecture); CaCoST (Creation and Conservation of SpaceTime).

Details: here we examine the little devils more closely!


This is the 10th ebook on MAP: mathematics—art—physics. All are available in Apple Books.

TPISC Media Resource Center

Yes, a deceptively simple matrix grid square (BIM) can give us:

1. Inverse Square Law (ISL);

2. Pythagorean Triples (PTs);

3. PRIMES (P)- Goldbach Conjecture!


This is an additional supplement to the MathspeedST ebook.

Other titles include The Pythagorean-Inverse Square Connection (TPISC):

TPISC I: Basics

TPISC II: Advanced

TPISC III: Clarity and the Tree of Primitive Pythagorean Triples



PTOP (Periodic Table Of PRIMES) and the Goldbach Conjecture



Get it on Apple Books

Excerpt From: Reginald Brooks. TPISC IV: Details, DSEQEC and PRIMES ” eBook.

Apple Books Store Link

Platforms: This is a multi-touch, interactive ebook made with iBooks Author and published in the Apple Books. 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 IV: Details, DSEQEC and PRIMES ebook

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

Artist Link in iTunes Apple Books Store: Reginald Brooks    



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 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

titles and topics:

LightspeedST: The Complete New Media project (HOME)

  • Page 60:     PTOP: Periodic Table Of PRIMES and the Goldbach Conjecture: How to Make with Fractals

  • Page 61:     PRIMES on the BIM

  • Page 62:     PRIMES on the BIM ebook

  • Page 63:     DSEQEC & CaCoST ebook

  • Page 64:    TPISC IV: Details, DSEQEC and PRIMES ebook

  • Page 65:     Math—Art—Physics (MAP) Index

    POB, PRIMES on the BIM, PTOP, Periodic Table Of PRIMES, PRIMES,NO-PRIMES, BIM, algebraic, algebraic geometry, Active Row Sets, AR, ARS, NON-Active Row, Number Pattern Sequence, NPS, 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
    PIN: Pattern in Number...from primes to DNA. | PIN: Butterfly Primes...let the beauty seep in. | PIN: Butterfly Prime Directive...metamorphosis. | PIN: Butterfly Prime Determinant Number Array (DNA) ~conspicuous abstinence~. | GoDNA: the Geometry of DNA (axial view) revealed. | SCoDNA: the Structure and Chemistry of DNA (axial view). | The LUFE Matrix | The LUFE Matrix Supplement | The LUFE Matrix: Infinite Dimensions | The LUFE Matrix: E=mc2 | Dark Matter=Dark Energy | The History of the Universe in Scalar Graphics | The History of the Universe_update: The Big Void | Quantum Gravity the book | The Conservation of SpaceTime | LUFE: The Layman's Unified Field Expose` | GoMAS: The Geometry of Music, Art and Structure ...linking science, art and esthetics. Part I | Brooks (Base) Square (BBS): The Architecture of Space-Time (TAOST) and The Conspicuous Absence of Primes (TCAOP) - a brief introduction to the series index | netart01: RealSurReal...aClone, 2001 | netart02: Hey!Ufunk'n with my DNA? | netart03: 9-11_remembered | netart04: Naughty Physics (a.k.a. The LUFE Matrix) | netart05: Your sFace or Mine? | netart06: Butterfly Primes | netart07: Music-Color-ISL | netart08: BBS-ISL matrix | netart09: BBS-interactive (I) | netart10: Sunspots and Solar Flares | netart11: Music-Color-ISL (II-III) | Art Theory 101: PIN, DNA, LUFE Matrix, GoMAS, BBS index | home
     Copyright 2020, Reginald Brooks, Brooks Design. All rights reserved.

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