After you set up your table with 10 x 10 Columns and Rows:

(Example using the Numbers app.)

A | B | C | E | F | G | H | I | J |

line | Axis # = x | PD # = x^{2} | x^{2} -1 | x^{2} -4 | x^{2} -9 | x^{2} -16 | x^{2} -25 | 36 |
---|

- Column Headers. After -25, simply copy and paste in the PD sequence 36-49-64-… that you can copy from your own list: 1
^{2}, 2^{2}, 3^{2}, 4^{2},... as found in Column 3 (C) below. - Column 2 (B) is just like Column 1 (A): type in 0,1,2,3… and drag down.
- POWER('Axis # = x',2) is the formula for squaring the Axis #s giving the PD#=x
^{2}in Column 3 (C). - $'PD # = x
^{2}'−1 is the formula for ALL the remaining Columns ADJUSTED by changing the “1” with the PD cell value found in the Header immediately above. The “$” symbol means “absolute” and all subsequent calcs will use the fixed value from C. - Once selected, you can drag-copy the formula across the Table and then make the ADJUSTMENTS quickly.
- Autofill the Table by selecting the TOP Row (under the HEADER) and pull down the orange-dot symbol to the bottom of the Table.
- Because the
**BIM**is bilaterally symmetrical about the PD, and, because the same PD #s forming the horizontal ROWS are also forming the vertical Columns, the**BIM**upper triangle — above the PD — will show a negative (-) sign in front of the cell values and this sign is to be ignored. - Below the PD, all the cell values will be (+) numbers, without any sign.
- The PD itself — because it reflects subtracting the same PD # from itself — will be “0” and this may be color coded to reflect that and/or the ACTUAL PD values, as found on the HEADER above, can be inserted.
- To expand or to fill in a particular Axis # — or range of #s — simply add the appropriate Columns and Rows and duplicate the above process for those values.

Color coding the Table, Columns, Rows and Cells can be done in the Numbers App Cell section. Text in the Text section, etc.

Why the 10th Column and Row? Fill that in to check your work here.

Larger examples of How to Make the BIM with a spreadsheet app (Numbers) found here in Table 31 series found in Appendix B ofOf course for smaller **BIM** grids, one can simply enter the cell values by hand as all the Inner Grid (IG) values are simply the difference between their Prime Diagonal (PD) Column and Row intercepts, e.i. 16 = 25 - 9 PD values.

BIM_How_to_Make from Reginald Brooks on Vimeo.

Open below image in a new tab to see all 5 example sheets.

- 1. Duplicate sheet made with the NEW method, rename new sheet;
- 2. On Row 2, replace with the NEW squared #s that you are extending;
- 3. On Row 3 (first non-header row), place the first formula and drag across:
- $'PD # = x2'−D$2
- 4. Drag Row 3 down to autofill the cells below. Each Col should have SAME formula, but will give individual values appropriate for its location. Double check. SAVE.
- 5. Color code the PD (Prime Diagonal “0”s), Row 3, and Col. C (blue) to separate out the Axis and PD from the Inner Grid cell values. Replace the PD #s with the Row 2 values, cente r all cells, and adjust format as needed.

BIM+PT (2018) Introduction from Reginald Brooks on Vimeo.

A central hub for all math works can be found on the MathspeedST Media Center page.

BIM 50x50 (open image in separate tab/window)

BIM 75x75 (open image in separate tab/window)

BIM 125x125 (open image in separate tab/window)

BIM 250x250 (open image in separate tab/window)

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BACK: ---> Part I of II CaCoST-DSEQEC on a separate White Paper
BACK: ---> Part II of II CaCoST-DSEQEC on a separate White Paper
BACK: ---> PRIMES vs NO-PRIMES on a separate White Paper
BACK: ---> TPISC_IV: Details_BIM+PTs+PRIMES on a separate White Paper
BACK: ---> TPISC IV: Details White Paper

Artwork referencing TPISC.

Artwork referencing TPISC.

Artist Link in iTunes Apple Books Store: Reginald Brooks

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KEYWORDS TAGS: TPISC, The Pythagorean - Inverse Square Connections, Pythagorean Triangles, DNA, Zika virus, pentagon, decagon, double pentagon, composite axial DNA double-helix, 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, DSEQEC, Double-Slit Experiment-Quantum Entanglement Conjecture, CaCost, Creation and Conservation of SpaceTime.

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