#educatorsandstudents

"tDMT-#1," digital, Sept. 2024, Reginald Brooks

The original DMT (Divisor Matrix Table) reveals ALL natural numbers and their divisors.

The truncated DMT -- tDMT -- is based on the original DMT, only filtered to reveal just those ODDs in Column 1 that are the Running Sums (∑) of the Row 1, i.e. 1-3-7-15-31-...

Why? The tDMT reveals ONLY those Rows that are "container" Rows -- i.e. based on the ∑s of the Exponential Power of 2 (seen as the Butterfly Fractal 1 sequence in Row 1)-- and these contain ALL possible Mersenne Prime-Perfect Number (Mp-PN) candidates.

Yes, that's a lot to swallow up front. One is simply taking the DMT and redacting out every Row except those beginning with 1-3-7-15-31-...

Why, again? The tDMT gives a simpler view of the key numbers informing the Mp-PNs!

The Mp-PNs are the rarest gems of the Primes!

BIMtree — ToPPT

2017-18, Reginald Brooks 

rbrooksdesign:

BIM+PT (2018) Introduction   Reginald Brooks

A very simple Introduction and Review of how to form the BBS-ISL Matrix (BIM), and, how ALL Pythagorean Triples (PTs) are located. It is part of TPISC IV: Details, coming on the heels of:

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 …

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:

An interactive version can be found at: 

Original soundtracks.

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

Click HERE for the TPISC — MathspeedST — BBS-ISL Matrix Media Center