Basic BBS-ISL Rule 1: All numbers (#s) related by the 1–4–9-…PD sequence
Basic BBS-ISL Rule 2: Every # in the PD sequence is the square of an Axial #.
Basic BBS-ISL Rule 3: The Odd-Number Summation sequence forms the PD sequence.
Basic BBS-ISL Rule 4: Every EVEN Inner Grid (IG) # is divisible by 4 & all are present.
A: The difference (∆) between its two PD-sequence #s. (Note: A=B=C=D=E, and F.)
B: The sum (∑) of the ∆s of each of its PD#s between its two PD-sequence #s (as above).
C: The ∆ between the squares of the two Axial #s forming that IG# (as above).
D: The product of the Addition & Subtraction of the two Axial #s forming that IG# (as above).
E: The product of the Diagonal Axis # — STEPS from the PD — times the ∑ of Row + Column Axis #s.
F: Also, the product of its 2 Axial #s intersected by that IG#’s 90° diagonals.
Basic BBS-ISL Rule 7: The ODD-Number sequence, and the 1–4–9-…PD sequence, forms the sequential ∆ between ALL IG#s.
Basic BBS-ISL Rule 8: The ∆ between #s within the Parallel Diagonals is a constant 2 x its Axial #.
Basic BBS-ISL Rule 10: Every #, especially the #s in the ONEs Column, informs both smaller and larger Sub-set symmetries (much larger grids required to demonstrate).
IGGR 1: The IG is formed of two equal & symmetrical 90°-right, isosceles triangles that are bilaterally symmetrical about the PD — and, infinitely expandable.
IGGR 2: The 90°-right-triangle — inherent to ALL squares and rectangles by definition — both forms the alternating EVEN-ODD square grid cells within the Matrix, and, is responsible for all major patterns and sequences, thereupon.
IGGR 3: Subtraction-Addition: Every IG# is simply the ∆ between its two PD#s (subtraction), and, the sum (∑) of any IG# + its PD# above = the PD# on the end of that Row (or, Column).
IGGR 4: Multiplication-Division: Every IG# is simply the product of the two AXIAL #s intersected by the two diagonals — of that said IG# — pointing back to the Axis at a 90° angle (multiplication), and, the dividend of the Axial divisor and quotient (division).
IGGR 5: The actual # of grid-cell steps — i.e., the actual # of STEPS from a given IG# to another by a strictly horizontal, vertical, or 45° diagonal path — forms a simple, yet often fundamental descriptor to the pattern-sequence templates that inform the more advanced patterns, e.i., Exponentials and especially the Pythagorean Triples (PTs). STEPS are particularly important in the geometric visualizations within the BBS-ISL Matrix (as alluded to in IGGR 2, above).
TPISC-BBS-ISL Rule 2: Every PT is found on the BBS-ISL Matrix and can be located by this intersection of EVERY PD (9>) and a Row with PFSs.
TPISC-BBS-ISL Rule 3: Every PT — including its sides, perimeter, area and proof — can also be found and fully profiled (and, predicted) as r-set, s-,t-set members of the Dickson Method (DM), Expanded Dickson Method (EDM), and the Fully Expanded Dickson Method (FEDM), shown herein.
White papers (freely available):
Works on pure mathematics include:
PIN: Pattern in Number…from primes to DNA (2001).
Butterfly Primes series (2005, 2006, 2006.)
GoDNA: the Geometry of DNA (2001).
GoMAS: The Geometry of Music, Art and Structure…linking science, art and esthetics (1987, 1996, 1998, 2009) with parts II and III (2012).
Brooks (Base) Square (BS): The Architecture of Space-Time (TOAST) and The Conspicuous Absence of Primes (TCAOP) - the complete work (Rules 1–177) (2009, 2010, 2011, 2012).
Brooks (Base) Square interactive (BBSi) Matrix: Part I: Basics (2011, 2013).
The Architecture of SpaceTime (TAOST) as defined by the Brooks (Base) Square Matrix and the Inverse Square Law (ISL) (2011).
Numbers Of Inevitability (2012).
AFPOP: A Fresh Piece of Pi(e)…and the √2, too…Fractal-Fractal-Fractal (2012).
The BBS-ISL Matrix papers, videos, slideshows, etc. all culminated in MathspeedST (2013) an interactive iBook, published in the iTunes iBooks Store. Free. Most of the white papers are freely available.
TPISC I: Basics: The Pythagorean - Inverse Square Connection – a MathspeedST Supplement (2015) an interactive iBook, published in the iTunes iBooks Store. Free. Most of the white papers are freely available.
TPISC II: Advanced: The Pythagorean - Inverse Square Connection – a MathspeedST Supplement (2015) an interactive iBook, published in the iTunes iBooks Store. Most of the white papers are freely available.
TPISC III: Simplification: The Pythagorean - Inverse Square Connection – a MathspeedST Supplement, Return to Basics – and then some (in progress, 2016–17).
BBS-ISL & TPISC Resources at:
BBS-ISL & TPISC Media Center at:
Interactive Matrix pages at:
Find Row-Col Axis number of Any IG number:
Find Row-Col Axis number of Any IG number:
Simple Visual Guide to making a BBS-ISL Matrix:
Simple Highlight Table Row/Col:
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