Symmetry—Fractals—Inverse Square Law

~A MathspeedST Supplement~

*Statement*

*Fractal–symmetry**Within the inverse square law**PPset entry*

Fractal — Symmetry —** Inverse Square Law** (**ISL**). These are not the usual descriptive terms associated with the Prime numbers (PRIMES) Yet that is exactly what best describes the PRIMES!

This come about as the well established PRIMES Sequence (PS) — 3-5-7-11-13-17-19-23-29-31-... acts in a fractal-like manner, i.e., it demonstrates redundant, repetitive and re-iterative behavior in presenting self-similar reflection of itself as it constructs PPsets and PPset “TRAILS.”

The TRAILS are formed from the concatenation of PS’s progressively onto each successive PRIME of a given PS — forming a series of PPsets along the way. The TRAILS can also be seen to be formed directly as individual PPsets on the **BIM**. Here, each PPset is easily seen to be intersection of 1 PPset member from the Horizontal AXIS and 1 PPset member from the Vertical AXIS, together forming the P_{1}, P_{2} members. The TRAIL is simply all those PPsets thus formed across a Row — or down a Column — on the bilaterally symmetrical **BIM**. All this is easily visible on the **BIM**.

That leads us to our story about the PRIMES—Fractals—Symmetry—and the intimate relationship they have with the **ISL** as seen on the **BIM**.

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

TPISC IV: Details, DSEQEC and PRIMES.

PRIMES vs NO-PRIMES

PTOP (Periodic Table Of PRIMES) and the Goldbach Conjecture

Excerpt From: Reginald Brooks. PRIMES on the BIM (POB) and the Goldbach Conjecture.” eBook.

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 PRIMES on the BIM (POB) and the Goldbach Conjecture*

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

Artist Link in iTunes Apple Books Store: 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****Page 56:****PRIME Gaps****Page 57:****PTOP: Periodic Table Of PRIMES and the Goldbach Conjecture****Page 58:****PTOP: Periodic Table Of PRIMES and the Goldbach Conjecture ebook in Apple Books****Page 59:****PRIMES Index PTOP: Periodic Table Of PRIMES, PRIMES Gap, PRIMES vs NO-PRIMES,...**

**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**

[ TOP ]

KEYWORDS TAGS: 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