Brooks (Base) Square (BS) 101

~ The Architecture of Space-Time (TAOST)

&

The Conspicuous Absence of Primes (TCAOP) ~

I.     TAOST / C. Geometrics – relationships / 2. Parallelogram

I. TAOST - the network

A. Geometrics – lines

B. Geometrics - shapes

C. Geometrics - relationships

1. Pythagorean

2. Parallelogram <---

3. Penta

II. TCAOP - everything minus the network

 TAOST: Rules 1-50 | Rules 51-80 | Rules 81-99 | Rules 100-107 | Rules 108-153 | TCAOP: Rule 154 | Rules 155-157 | Rules 158-159 | Rule 160 | Interconnectedness: Rules 161-175 | Appendix A: Rules 176-181 | Appendix B: Rules 182-200 |

I C. Geometrics - Relationships - 2.Parallelograms

Part 2- Parallelograms

Much of the work on parallelograms essentially laid down the early pathways to the magic kingdom of the “Penta,” that we will be looking at in great detail in the next section. “Parallelogram” started out by looking at the sums of the differences between the columns.

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100

BS Rule 100: The difference, ∆, in the sums, ∑, of the difference in all members of a given row increase by subsequent sums expansion as 2, 4, 8, 16, 32,....

Note:

 ∆ in Row  Differnces ∆ sequentially across rows # values in Columns B, C, D, ... 2 4 8 16 32 3   5   7   9   11   13   15   17   19   21   23   25 ∑ of those ∆ sequentially across rows # values in Columns B, C, D, ... 8  12  16  20  24  28  32  36  40  44  48 ∑ of those ∆ sequentially across rows # values in Columns B, C, D, ... 20 28 36 44 52 60 68 76 84 92 ∑ of those ∆ sequentially across rows # values in Columns B, C, D, ... 48 64 80 96 112 ∑ of those ∆ sequentially across rows # values in Columns B, C, D, ... 112 144 176 208

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101

BS Rule 101: On the vertical axis, adding up the number of values 1-10, the sum, ∑, is 55. If we only add the values of the 1st number (the ‘ones” column value) and disregard the 2nd number (the “tens” column value), the ∑Col A=45. Likewise, examining the ∑ of the first ten number values of Column B, C, D, ... we end up with a parallelogram pattern that repeats on every 5th column across and every 10th row down the Inner Grid.

Note:

 Column B, C, D, ... ∑Col B, C, D, ... 1st # values B 45 ⬆ | | | | | C 35 D 35 E 45 F 45 Symmetry line G 45 | | | | | ⬇ H 35 I 35 J 45 K 45 Symmetry line

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102

BS Rule 102: A strict mirror symmetry line of 1st number values exists across every 5-based row (axis # is evenly divisible by 5) in the Inner Grid as each and every column value progresses up and down.

Note:

 5-based Axis # Column B Column C ( 0) - ⬆ | | | | | 3 ( 0) 8 5 1 5 1 2 5 2 4 2 1 Symmetry line 3 5 3 2 | | ⬇  ⬆ | | 4 8 4 5 6 3 6 0 8 0 7 7 10 9 9 9 6 Symmetry line 12 0 11 7 | | ⬇  ⬆ | | 14 3 14 0 16 8 16 5 19 5 19 2 15 22 4 22 1 25 5 25 2 | | ⬇  ⬆ | 28 8 28 5 32 3 32 0

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 ~click to enlarge image 103 BS Rule 103: The diagonal border line (paralleling the PD) describing each major parallelogram extends at a 45〫angle from the 0, 10, 20, 30, ...axis value to its vertices grid point, 5 columns away, at (*25), 200, 600, 1200, ..., respectively. (*25): Note that 25 is on the PD. The Inner Grid pattern does not apply here or in other circumstances in which the Inner Grid pattern butts up to or overlaps the PD. Note: The minor, mirrored parallelogram within each major parallelogram runs from the 5, 15, 25,... axis value to the 75, 375, 875,... respective internal vertices. Restated: The parallelogram diagonals run even-to-even and odd-to-odd values, all of which are multiples of 5. Within the matrix, multiples of 5 (5-based) are the dominant focus points.

 ~click to enlarge image 104 BS Rule 104: Similarly, parallelogram diagonals that run perpendicular to the PD, crossing (dividing) each major parallelogram, vertices to vertices, at its halfway point ... but do so by running alternately even-to-odd, even-to-even while going through the 5-based focus points. The minor parallelogram diagonals run odd-to-odd, finishing on the 1st Diagonal (not on the PD) with the same value as on the axis, as 5-5, 15-15, 25-25, .... Note: This pattern focuses on multiples of 5. Difference, ∆, steps.

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 ~click to enlarge image 105 BS Rule 105: The Inner Grid focus points, that all the major and minor parallelogram diagonals cross, are all multiples of 5 . These focus point are the subject of the next section (see “Penta”). They form diamond-square shapes when linked by the diagonals of parallelograms and they form straight squares when linked straight across rows. Of particular note here ... and of great interest in the “Penta” section ... is that these “nodes” of multiples of 5 are exclusively symmetrical to the 1st number value along all three ... really, four ... node axes ... horizontal, vertical and diagonal (both ways). An even larger, major symmetry line occurs at (52)2 = 252 = 625 PD.

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106

BS Rule 106: The larger column symmetry of the 1st  (“ones”)

number values, while symmetrical at the 25-625 row and column lines, additionally, repeats symmetrically outward from each 5-based column.

Note: Restated: The larger interference pattern centered on the 25 x 25 = 625 column-row lines is harmonically subdivided into smaller resonant interference patterns at every 5th (5-based) column and row. Additionally, the subdivided symmetry value pattern repeats on every other row. The vertical columns repeat, in a staggered fashion, at Columns B&J and E&G, and Columns C&I, and D&H, and Columns F&K, the latter forming a larger yet symmetry that the former are mirrored out from.

 ⬅------------ Symmetry line --------➜⬅---------- Symmetry line B J E G C I D H F K

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107

BS Rule 107: The larger row symmetry of the 1st  (“ones”) number values can best be seen in an expanded view of Brooks (Base) Square.

Note:

 ⬅------------ Symmetry line --------➜⬅---------- Symmetry line 0 5         10      15         20 25 30       35       40       45 50 5 25 ⬆ | | | | | 10 100 15 225 20 ⬆ ⬆ ⬆ 400 25 600 ⬅ 525 ⬅ 400 ⬅ 225 ⬅ 625 ➜ ➜ ➜ ➜ 30 ⬇ ⬇ ⬇ 500 | | ⬇  ⬆ | 900 35 1000 1225 40 1500 1600 45 2000 2025 50 2500

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 TAOST: Rules 1-50 | Rules 51-80 | Rules 81-99 | Rules 100-107 | Rules 108-153 | TCAOP: Rule 154 | Rules 155-157 | Rules 158-159 | Rule 160 | Interconnectedness: Rules 161-175 | Appendix A: Rules 176-181 | Appendix B: Rules 182-200 |

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Page 2a- PIN: Pattern in Number...from primes to DNA.

Page 2b- PIN: Butterfly Primes...let the beauty seep in..

Page 2c- PIN: Butterfly Prime Directive...metamorphosis.

Page 2d- PIN: Butterfly Prime Determinant Number Array (DNA) ~conspicuous abstinence~.

Page 3- GoDNA: the Geometry of DNA (axial view) revealed.

Page 4- SCoDNA: the Structure and Chemistry of DNA (axial view).

Page 5a- Dark-Dark-Light: Dark Matter = Dark Energy

Page 5b- The History of the Universe in Scalar Graphics

Page 5c- The History of the Universe_update: The Big Void

Page 6a- Geometry- Layout

Page 6b- Geometry- Space Or Time Area (SOTA)

Page 6c- Geometry- Space-Time Interactional Dimensions(STID)

Page 6d- Distillation of SI units into ST dimensions

Page 6e- Distillation of SI quantities into ST dimensions

Page 7- The LUFE Matrix Supplement: Examples and Proofs: Introduction-Layout & Rules

Page 7c- The LUFE Matrix Supplement: References

Page 8a- The LUFE Matrix: Infinite Dimensions

Page 9- The LUFE Matrix:E=mc2

Page 10- Quantum Gravity ...by the book

Page 11- Conservation of SpaceTime

Page 12- LUFE: The Layman's Unified Field Expose`

Page 13- GoMAS: The Geometry of Music, Art and Structure ...linking science, art and esthetics. Part I

Page 14- GoMAS: The Geometry of Music, Art and Structure ...linking science, art and esthetics. Part II

Page 15- Brooks (Base) Square (BS): The Architecture of Space-Time (TAOST) and The Conspicuous Absence of Primes (TCAOP) - a brief introduction to the series

Page 16- Brooks (Base) Square interactive (BBSi) matrix: Part I "BASICS"- a step by step, multi-media interactive

Page 17- The Architecture Of SpaceTime (TAOST) as defined by the Brooks (Base) Square matrix and the Inverse Square Law (ISL).