"TPISC III: Clarity"
Tree of Primitive Pythagorean Triples (ToPPT) Logo

BIMtree — ToPPT from Reginald Brooks on Vimeo.

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 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 (my) 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 …

This video and original music is simply a montage of the digitally painted ToPPT logo.

Please visit brooksdesign-ps.net New Media webpage to see more.

This work is for TPISC III: Clarity and Simplification: The Tree of Primitive Pythagorean Triples (ToPPT), copyright 2017, Reginald Brooks. It comes in html, PDF and iBooks formats.

The Pythagorean — Inverse Square Connection (TPISC) is a series of Supplements to the original MathspeedST work:

TPISC I: Basics
TPISC II: Advanced
TPISC III: Clarity
TPISC IV: Details (coming)
TPISC V: Exponentials (coming)


There are some 11 videos on MathspeedST: BASICS for TES (Teachers, Educators and Students) on Vimeo.
See links below for more information on the BBS-ISL matrix.

The full version of the BBS-ISL matrix grid—including visuals on all 200 Rules can be found on my website at:
http:// www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/ISL/Brooks_(Base)_Square/netart95.htm

An interactive version can be found at:
http://www. brooksdesign-ps.net/Reginald_Brooks/Code/Html/ISL/BBS/BBSiI.html

A new white paper on "The Ubiquitous Information of Numbers" ( or "How Fractals can exceed the speed limit of light)
http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/MSST/MathspeedST_uin.html

A new media net.art project on the same subject at:
http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/netart16.htm

The significance of the BBS-ISL matrix is that it provides a form of ubiquitous information that permeates the Universe below the formation of spacetime itself, in effect, providing information faster than the speed of light!

The complete works have been aggregated into the freely available "MathspeedST: Leapfrogging LightspeedST FASTER Than The Speed of Light" ebook.
http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/MSST/MathspeedST_eBook.html

This work complements "LightspeedST: Leapfrogging @ The Speed of Light," and the essence of this ibook can also be found freely available at:
http://www. brooksdesign-ps.net/Reginald_Brooks/Code/Html/LSST/netart14.htm

https://itunes.apple.com/us/author/reginald-brooks/id657634078?mt=11

Original soundtracks.
Thanks for taking a look! Check out the links to get the full load.