BBS-ISL Matrix

To find the Row/Column placement of any Inner Grid ( IG) number (#):


1. find Factors
2. add Factors, divide by 2 = Row #
3. confirm by determining Col # 
    * a. divide IG # by larger Factor (or simply take the smaller Factor)
    * b. subtract  the resulting quotient from the Row # = Col #
    * c. verify by finding the ∆ between the two PD #s

Ex: 33 (Two Factor Sets, example for Factor Set: 3,11 only*)

Factors: 3, 11—(1,33)
Row: 3 + 11 = 14, 14 ÷ 2 = 7 = Row 7
Column - confirm & verify:
- a. Divide: 33 ÷ 11 = 3
- b. Subtract: 7 - 3 = 4 = Col 4
- c. verify: 7² - 4² = 49 - 16 = 33

Therefore: IG# 33 appears 2 times on the IG at:

Row 7, Col 4
Row 17, Col 16(*see note @ bottom)

Ex: 96 (Five Factor Sets, example for four Factor Sets only)

Factors: 2,48—3,32—4,24—8,12—(1,96)
Row:
- 2 + 48 = 50, 50 ÷ 2 = 25 = Row 25
- 3 + 32 = 35, 35 ÷ 2 = 17.5 = RowXXXX (Is NOT whole integer #)
- 4 + 24 = 28, 28 ÷ 2 = 14 = Row 14
- 8 + 12 = 20, 20 ÷ 2 = 10 = Row 10
Column - confirm & verify:
- a. Divide:
  - 96 ÷ 48 = 2
  - xxx skip because not whole integer #
  - 96 ÷ 24 = 4
  - 96 ÷ 12 = 8
- b. Subtract:
  - 25 - 2 = 23 = Col 23
  - xxx
  - 14 - 4 = 10 = Col 10
  - 10 - 8 = 2 = Col 2
- c. verify:
  - 25² - 23² = 625 - 529 = 96
  - xxx
  - 14² - 10² = 196 - 100 = 96
  - 10² - 2² = 100 - 4 = 96

Therefore: IG# 96 appears 4 times on the IG. The three examples at:

Row 25, Col 23
Row/Col XXX skip because not whole integer #)
Row 14, Col 10
Row 10, Col 2
(*see note @ bottom re: 1,96)

SIMPLIFICATION

SIMPLIFICATION;
 1. ∑ Factors ÷ 2 = Row #
 2. Row # - Factor # = Col #
 3. verify PD - PD = IG#

Ex: 96 (Factors: 1,96—2,48—3,32—4,24—8,12)

Factors: 2,48

∑ Factors ÷ 2 = Row #:
- (2 + 48) ÷ 2= Row 25
Row # - Factor # = Col #:
- 25 - 2 = Column 23
verify PD - PD = IG#:
- 25² - 23² = 625 - 529 = 96

Therefore: IG# 96 appears on the IG at:

Row 25, Col 23

Factors: 3,32

∑ Factors ÷ 2 = Row #:
- xxx (no IG# with this Factor Set)

Factors: 4,24

∑ Factors ÷ 2 = Row #:
- ( 4 + 24) ÷ 2= Row 14
Row # - Factor # = Col #:
- 14 - 4 = Column 10
verify PD - PD = IG#:
- 14² - 10² = 196 - 100 = 96

Therefore: IG# 96 appears on the IG at:

Row 14, Col 10

Factors: 8,12

∑ Factors ÷ 2 = Row #:
- ( 8 + 12) ÷ 2= Row 10
Row # - Factor # = Col #:
- 10 - 8 = Column 2
verify PD - PD = IG#:
- 10² - 2² = 100 - 4 = 96

Therefore: IG# 96 appears on the IG at:

Row 10, Col 2

Ex: 1125

Factors: (1, 1125)

Factors: (3, 375)

Factors: (5, 225)

Factors: (9, 125)

Factors: (15, 75)

Factors: (25, 45)

∑ Factors ÷ 2 = Row #:
- (1 + 1125) ÷ 2 = Row 563
- ( 3 + 375) ÷ 2 = Row 189
- ( 5 + 225) ÷ 2 = Row 115
- ( 9 + 125) ÷ 2 = Row 67
- ( 15 + 75) ÷ 2 = Row 45
- ( 25 + 45) ÷ 2 = Row 35
Row # - Factor # = Col #:
- Row 563 - 1 = Col 562
- Row 189 - 3= Col 186
- Row 115 - 5 = Col 110
- Row 67 - 9 = Col 58
- Row 45 - 15 = Col 30
- Row 35 - 25 = Col 10
verify by PD - PD = IG#:
- 563² - 562² = 316,969 - 315,844 = 1125
- 189² - 186² = 35,721 - 34,596 = 1125
- 115² - 110² = 13,225 - 12,100 = 1125
- 67² - 58² = 4,489 - 3,364 = 1125
- 45² - 30² = 2,025 - 900 = 1125
- 35² - 10² = 1,225 - 100 = 1125

Therefore: IG# 1125 appears 6 times on the IG at:

Row 563, Col 562
Row 189, Col 186
Row 115, Col 110
Row 67, Col 58
Row 45, Col 30
Row 35, Col 10

*The Factor Set that includes 1,X where X = the IG#, 
ALWAYS lies on the 1st Parallel Diagonal (3,5,7,..) if ODD;
and,if X=EVEN IG#, it will NOT be on the matrix grid, as 1+EVEN # = ODD #,
e.i. IG# 33 using Factor Set 1,33 resolves to Row 17 Col 16, 
while IG# 8 does NOT have a Row/Col presence with Factor Set 1,8 as it does NOT resolve to a whole number.

References

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).
Brooks (Base) Square -10. Copyright© 2016, Reginald Brooks. All rights reserved.

Images

Highlight Interactive BBS-ISL Matrix at:

BBS-ISL_Matrix10x10_TableRowColHighlight.html

BBS-ISL_Matrix20x20_TableRowColHighlight.html

BBS-ISL_Matrix35x35_TableRowColHighlight.html

BBS-ISL_Matrix35x35-LARGE_TableRowColHighlight.html
BBS-ISL_Matrix50x50-LARGE-Highlight.html

BBS-ISL_Matrix50x50-LARGE.html

BBS-ISL & TPISC Resources at:

MSST-TPISC_resources/netart19.htm

BBS-ISL & TPISC Media Center at:

MediaCenter_MSST-TPISC_resources.html

Interactive Matrix pages at:

BBS-ISLi.html

BBS/BBSiI.html

Brooks (Base) Square matrix (BBS) interactive BBS-ISL hands-on matrix grids

BBS-ISL_Matrix: Simplified.html

*****
Find Row-Col Axis number of Any IG number:

BBS_FindRow-Col_Any_IG_number.pdf

BBS_FindRow-Col_Any_IG_number.html

Find Row-Col Axis number of Any IG number:

BBS_ToFindRow-ColAnyIGnumber.pdf

BBS_ToFindRow-ColAnyIGnumber.html

BBS_ToFindRow-ColAnyIGnumber-MARP.pdf

BBS-ISL_IGGR_TPISC_fundamental_rules:

BBS-ISL_IGGR_TPISC_rules.html

BBS-ISL_IGGR_TPISC_rules.pdf

BBS-ISL_IGGR_TPISC_rulesMARP.pdf

BBS-ISL_Matrix_Overview Slideshow:

BBS-ISL_Matrix_Overview_MARP.pdf

Simple Visual Guide to making a BBS-ISL Matrix:

BBS-ISL10x10+.html

Simple Highlight Table Row/Col:

highlightTableRowCol_BBBS-ISL.html

highlightTableRowCol_BBBS-ISL10x.html

highlightTableRowCol_BBBS-ISL20x.html

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Images

KEYWORDS TAGS: TPISC, The Pythagorean - Inverse Square Connections, Pythagorean Triangles, Pythagorean Triples, primitive Pythagorean Triples, non-primitive Pythagorean Triples, Pythagorean Theorem, Pythagorus Theorem, The Dickson Method, BBS-ISL Matrix, Expanded Dickson Method, r-sets, s-set, t-sets, Pair-sets, geometric proofs, MathspeedST, leapfrogging LightspeedST FASTER than the speed of light, Brooks (Base) Square- Inverse Square Law (ISL), BBS-ISL Matrix grid, The Architecture Of SpaceTime (TAOST), The Conspicuous Absence Of Primes (TCAOP), A Fresh Piece Of Pi(e), AFPOP, Numbers of Inevitability, LightspeedST, Teachers, Educators and Students (TES), number theory, ubiquitous information, FASTER than the speed of light, primes, prime numbers, fractals, mathematics, Universe, cosmos, patterns in number.

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Copyright 2016-17, Reginald Brooks, Brooks Design. All rights reserved.

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