TPISC III:

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)

This is a multi-touch, interactive ebook made with Apple’s iBooks Author software and published in the Apple iBooks Store.