Brooks (Base) Square (BS) 101
~ The Architecture of SpaceTime (TAOST)
&
The Conspicuous Absence of Primes (TCAOP) ~
I. TAOST / B. Geometrics  shapes
I. TAOST  the network
B. Geometrics  shapes <
II. TCAOP  everything minus the network
TAOST: Rules 150  Rules 5180  Rules 8199  Rules 100107  Rules 108153  TCAOP: Rule 154  Rules 155157  Rules 158159  Rule 160  Interconnectedness: Rules 161175  Appendix A: Rules 176181  Appendix B: Rules 182200  
I B. Geometrics  Shapes
There are two parts to this section on shapes. In the first part, we will be looking at shapes formed of diagonal lines within the grid. To illustrate these numerical relationships, we will be using the original Base Square (BS 1.00). The exact symmetry of the lower and upper triangles in the base version of the matrix grid show the patterns to the best advantage.
In the second part, individual geometric shapes will be the focus. For this part, we will revert back to the default Brooks Square (BS 1.01+) version.
Part 1 shaped by diagonals within the grid (BS 1.00).
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TAOST: Rules 150  Rules 5180  Rules 8199  Rules 100107  Rules 108153  TCAOP: Rule 154  Rules 155157  Rules 158159  Rule 160  Interconnectedness: Rules 161175  Appendix A: Rules 176181  Appendix B: Rules 182200  
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TAOST: Rules 150  Rules 5180  Rules 8199  Rules 100107  Rules 108153  TCAOP: Rule 154  Rules 155157  Rules 158159  Rule 160  Interconnectedness: Rules 161175  Appendix A: Rules 176181  Appendix B: Rules 182200  
Part 2 individual shapes within the grid (BS 1.01+).
Triangles
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62  BS Rule 62: Any equilateral triangle formed in Column C, and labeled A (top), B, © and C, will have the difference, ∆, between the sums, ∑, A+B+© and A+C+© is 8. Simplified: BC=8 
Note: This follows from BS Rule 31, where the ∆ in number values from Column B to C=3, Column C to D=5, Column D to E=7,... and therefore, Column B to D=8 as the columns decrease in value by 1, 3, 5, ...left to right, respectively. 
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63  BS Rule 63: The same Rule 62 in reverse, A, ©, B and C (bottom) is true. 
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64  BS Rule 64: Following BS Rule 31 ... and similar to Rules 62 and 63 above ... as one moves the triangle to the right, Columns D, E, F,... the difference, ∆, in values goes as: 12, 16, 20, ... 
Note: C to E=12, D to F=16, E to G=20, ... and so on. 
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Square and Rectangles
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65  BS Rule 65: Additions of opposite diagonal number values of any rectangle parallel to the grid axis, are equal. 

Note:

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DiamondSquares
TAOST: Rules 150  Rules 5180  Rules 8199  Rules 100107  Rules 108153  TCAOP: Rule 154  Rules 155157  Rules 158159  Rule 160  Interconnectedness: Rules 161175  Appendix A: Rules 176181  Appendix B: Rules 182200  
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66  BS Rule 66: The difference, ∆, in the sums, ∑, of the opposite diagonal values of any 2x2 grid point unit diamondsquares = 4, or 2^{2} 

Note:

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67  BS Rule 67: The central number value, ©, of any square or diamondsquare equals the sum, ∑, of the perimeter number values divided by the number (quantity, #) of perimeter units, punits. 

Note: ∑_{punits} ÷ #_{punits} = ©

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68  BS Rule 68: The difference, ∆, in the sums, ∑, of the opposite diagonal number values of any 3x3 grid point unit diamondsquares = 16, or 4^{2}. 

Note:

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69  BS Rule 69: The central number value, ©, of any square or diamondsquare equals the sum, ∑, of opposite side perimeter number values divided by the number (quantity, #) of perimeter units, punits. 

Note: ∑_{punits} ÷ #_{punits} = ©

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70  BS Rule 70: The difference, ∆, in the sums, ∑, of the opposite diagonal number values of any 4x4 grid point unit diamondsquares = 36, or 6^{2}. 

Note:

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TAOST: Rules 150  Rules 5180  Rules 8199  Rules 100107  Rules 108153  TCAOP: Rule 154  Rules 155157  Rules 158159  Rule 160  Interconnectedness: Rules 161175  Appendix A: Rules 176181  Appendix B: Rules 182200  
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71  BS Rule 71: The central number value, ©, of any square or diamondsquare equals the sum, ∑, of opposite side perimeter number values divided by the number (quantity, #) of perimeter units, punits. 

Note: ∑_{punits} ÷ #_{punits} = ©

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72  BS Rule 72: The central number value, ©, of any square or diamondsquare equals the sum, ∑, of symmetrically opposite individual perimeter number values divided by the number (quantity, #) of perimeter units, punits. 

Note: ∑_{punits} ÷ #_{punits} = ©

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73  BS Rule 73: The difference, ∆, in the sums, ∑, of the opposite diagonal number values of any 5x5 grid point unit diamondsquares = 64, or 8^{2}, and so on. 

Note:

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74  BS Rule 74: As in Rules 69, 71, and 72, as the number of perimeter units increase, so do the number of combinations of symmetrically opposite punit number values that, when divided by the # of punits, will = ©. 

Note:

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75  BS Rule 75: Combining the perimeter number values of diamondsquares 2x2, 3x3, 4x4,and 5x5, and dividing by the total number,#, of punits = ©. 

Note: ∑_{punits} ÷ #_{punits} = ©

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TAOST: Rules 150  Rules 5180  Rules 8199  Rules 100107  Rules 108153  TCAOP: Rule 154  Rules 155157  Rules 158159  Rule 160  Interconnectedness: Rules 161175  Appendix A: Rules 176181  Appendix B: Rules 182200  
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76  BS Rule 76: For a given central number, ©, its horizontal Prime Diagonal, PD_{h}, number value minus it vertical, PD_{v, }number value = ©. 

Note: PD_{h}PDv=© as 10025=75 Restated: PD_{h}Column Value=PD_{v}

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77  BS Rule 77: For a given central number, ©, the difference,∆, between it and the 1^{st} vertical number value above it is found on the 1^{st }Diagonal intersecting that row. For a given central number, ©, the difference,∆, between it and the 2^{nd }vertical number value above it is found on the 2^{nd }Diagonal intersecting that rowr. For a given central number, ©, the difference,∆, between it and the 3^{rd} vertical number value above it is found on the 3^{rd }Diagonal intersecting that row, and so on. 

Note: Restated: The ∆ between © and the column # value above, can be found on the row of its PD_{h}.

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78  BS Rule 78: Similarly, for a given central number, ©, the difference, ∆, between it and the 1^{st} horizontal row number towards the PD is found vertically in the column above © on the 1^{st} Diagonal intersecting that column. For a given central number, ©, the difference, ∆, between it and the 2^{nd} horizontal row number towards the PD is found vertically in the column above © on the 2^{nd} Diagonal intersecting that column. For a given central number, ©, the difference, ∆, between it and the 3^{rd} horizontal row number towards the PD is found vertically in the column above © on the 3^{rd} Diagonal intersecting that column, and so on. 

Note: Restated: The ∆ between © and the row # towards the PD, can be found on the column of its PD_{v}.

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79  BS Rule 79: Similarly, for a given central number, ©, the difference, ∆, between it and the 1^{st} horizontal row number away from the PD is found vertically in the column above that 1^{st} horizontal row # on the 1^{st} Diagonal intersecting that column. For a given central number, ©, the difference, ∆, between it and the 2^{nd} horizontal row number away from the PD is found vertically in the column above that 2^{nd} horizontal row # on the 2^{nd} Diagonal intersecting that column. For a given central number, ©, the difference, ∆, between it and the 3^{rd} horizontal row number away from the PD is found vertically in the column above that 3^{rd} horizontal row # on the 3^{rd} Diagonal intersecting that column, and so on. 

Note: Restated: The ∆ between © and the row # away from the PD, can be found on the row of its respective vertical PD_{v}.

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80  BS Rule 80: Similarly, for a given central number, ©, the difference, ∆, between it and the 1^{st} vertical column number below, away from the PD is found horizontally in the row where the the 1^{st} Diagonal intersects. For a given central number, ©, the difference, ∆, between it and the 2^{nd} vertical column number below, away from the PD is found horizontally in the row where the the 2^{nd} Diagonal intersects. For a given central number, ©, the difference, ∆, between it and the 3^{rd} vertical column number below, away from the PD is found horizontally in the row where the the 3^{rd} Diagonal intersects. 

Note: Restated: The ∆ between © and the column of #s below, away from the PD, can be found on the column below ©’s respective horizontal PD_{h}.

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TAOST: Rules 150  Rules 5180  Rules 8199  Rules 100107  Rules 108153  TCAOP: Rule 154  Rules 155157  Rules 158159  Rule 160  Interconnectedness: Rules 161175  Appendix A: Rules 176181  Appendix B: Rules 182200  
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I. TAOST>IC. Geometricsrelationships Brooks (Base) Square
Back to I. TAOST>IA. Geometricslines  Brooks (Base) Square
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 DarkDarkLight: 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 SpaceTime 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: IntroductionLayout & Rules
Page 7c The LUFE Matrix Supplement: References
Page 8a The LUFE Matrix: Infinite Dimensions
Page 9 The LUFE Matrix:E=mc^{2}
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 SpaceTime (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, multimedia interactive
Page 17 The Architecture Of SpaceTime (TAOST) as defined by the Brooks (Base) Square matrix and the Inverse Square Law (ISL).
The LUFE Matrix  The LUFE Matrix Supplement  The LUFE Matrix: Infinite Dimensions  The LUFE Matrix: E=mc^{2}  Dark Matter=Dark Energy  The History of the Universe in Scalar Graphics  The History of the Universe_update: The Big Void  Quantum Gravity ...by the book  The Conservation of SpaceTime  LUFE: The Layman's Unified Field Expose`  
net.art index  netart01: RealSurReal...aClone  netart02: funk'n DNA/Creation GoDNA  netart03: 911_remembered  netart04: Naughty Physics (a.k.a. The LUFE Matrix)  netart05: Your sFace or Mine?  netart06: Butterfly Primes  netart07: Geometry of Music Color  net.games  Art Theory 101 / White Papers Index  