TPISC II: The Pythagorean - Inverse Square Connection: Advanced

The Pythagorean - Inverse Square Law Connection — or how the Pythagorean Theorem is intimately embedded within the The Architecture Of SpaceTime (TAOST) as described by the BBS-ISL Matrix is first and foremost the topic of this book.

This work is being presented precisely because the very nature of that geometric relationship of the Pythagorean Triangle (PT) is so intimately related to the Inverse Square Law (ISL), as depicted in the BBS-ISL Matrix, that a cause and effect relationship between the two is unavoidable.

That the BBS-ISL Matrix also provides the simplest, most intuitively obvious proof to the Theorem directly on the grid only supports the argument. Every possible PT, and its proof, is visually and mathematical present. The Dickson Method confirms this.

TPISC I: Basics
TPISC I: The Pythagorean - Inverse Square Connection: Basics revealed the presence, proofs and and overall distribution of the Pythagorean Triples (PTs) upon the BBS-ISL Matrix. The distribution was shown as occurring on, and only on, each and every Row/Column that contained AREA Squares. Scan the Rows and if they contained Pair-Sets of these AREA Squares you would always find a PT there.

TPISC II: Advanced
TPISC II: The Pythagorean - Inverse Square Connection: Advanced profoundly enlarges upon the Dickson Method — giving the Extended Dickson Method — which has opened the doors to the real connection between the ISL and the PTs. Patterns of Fractal-like Relationships, is a descriptive phrase loaded with the implications that the PTs, while ubiquitously embedded throughout the infinite BBS-ISL Matrix, grow within it in a profoundly fractal-like pattern. Parsing these into r-set and s-set groups becomes key in determining the pattern distribution of ALL PTs.

Every grid cell # within the BBS-ISL Matrix is determined by the Prime Diagonal #s, as is every possible PT.

The PTs, just like the circle and square, define the ISL!

So in the end, what are we to make of all this?
Why the BBS-ISL matrix — which begs the question: Why the Inverse Square Law (ISL) — and why the
Pythagorean Triples?

And so what if they are both made up of whole integer #s?
And so what if they both expand to infinity?
And so what if the the PTs seem to be all inter-connected?
And so what if the Pts seem to be infinitely embedded within the BBS-ISL matrix?
And so what if there is a pattern to how they are embedded?
And so what if they both share a common pattern of 90° right-angle isosceles triangle relationships?
And so what if the ISL informs all of SpaceTime?
And so what if the ISL thus informs all expressions of energy as matter & waves — particles & fields?
And so what if all such interactions — including those of growth — is predicated on the unfolding of the ISL-dependent SpaceTime?
And so what if those simple PTs — pattern- peppered throughout the BBS-ISL matrix — are laying down networking nodes of optimal 90° right-angle connections amongst the more widely distributed ISL background structure

Are not the PTs there to organize it all?

TPISC, The Pythagorean — Inverse Square Connection, is about shining some light on how Nature ubiquitously builds combining simple, elemental forms into sentient constructs able to reflect the light all the way back home!