Making the BIM — any size BIM — in the Numbers App or other Spreadsheet Apps
Numbers App Instructions:
・To grow PD Col, select and expand to the bottom and then fill left column by autofill, PD column will auto fill from this.
・$’PD # = x2’−16 is the formula for expanding Columns — where PD # equals the SQUARED Axis #, designated as “x”. (Must change 16—>25,36,49,… to fill out the grid.)
・Here the resulting PD = Blue 0. One may insert the ACTUAL PD # values — 1-4-9-16-25-…— into the “0” field to complete the BIM. The Column header contains the PD value. ・The negative (-) cell values above the PD result from the formula and the “-“ is to be ignored. The BIM is completely mirror-symmetric from the PD. ・See PD Sequence _vertical-Col and _horizontal-Row.numbers for easy access to PD2 from 1-200. One can make a 200×200 BIM, by adding columns out to x2 – 40000, i.e., Axis Column 200.
IN MORE DETAIL. Following the TABLE 31a_++ or +++ Numbers app
1. Column Headers:
line
Axis # = x
PD # = x2
x2 -1
x2 -4
x2 -9
x2 -16
x2 -25
36
1.Column Headers. After -25, simply copy and paste in the PD sequence 36-49-64-….
2. Column 2 (B) is just like Column 1 (A): type in 0,1,2,3… and drag down.
3. POWER(‘Axis # = x’,2) is the formula for squaring the Axis #s giving the PD#=x2 in Column 3 (C).
4. $’PD # = x2’−1 is the formula for ALL the remaining Columns ADJUSTED by changing the “1” with the PD cell value found in the Header immediately above. The “$” symbol means “absolute” and all subsequent calc will use the fixed value from C.
5. Once selected, you can drag-copy the formula across the Table and then make the ADJUSTMENTS quickly.
6. Autofill the Table by selecting the TOP Row (under the HEADER) and pull down the orange-dot symbol to the bottom of the Table.
7. 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.
8. Below the PD, all the cell values will be (+) numbers, without any sign.
9. 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.
10. 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.
~~~~formulas used (Numbers)~~~~
fx (B):
POWER(‘Axis # = x’,2)
fx (C):
$’PD # = x2’−1
fx:
$’PD # = x2’−4
fx:
$’PD # = x2’−9
fx:
$’PD # = x2’−16
fx:
$’PD # = x2’−25
fx:
$’PD # = x2’−36
BIM = BBS-ISL Matrix. The BIM is a simple, yet remarkably well-connected, matrix grid built on the Inverse Square Law (ISL). It only uses Whole Integer Numbers (WINs). It extends to infinity.
The BIM is inter-related to the Pythagorean Triples, as well as the PRIMES. They both go to infinity.
TPISC, the Pythagorean-Inverse Square Connection, is a large ongoing project of many years. It has generated a large number of videos (Vimeo), graphics and supporting white papers that may be referenced at:
http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/MSST/MSST-TPISC_resources/MSST-TPISC_resources.html the portal page of the BBS-ISL Matrix media center.
Using your own spreadsheet app, you can now easily generate any size BIM and/or any particular Column/Row. Customize it as it suites your needs and desires. And it is searchable.
Original soundtrack.
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