16 Variable Octagon Projected from Hypercube
Do you think it is allready in binairy? Estimated calculation time by hand unknown.
Combinatoric alg for the Octagon applies in this case.
Download XL file:
Octagon from Hypercube.xls
These spreadsheet calculations are wildly accurate, not unlike the rest. It is a fairly quantitative perfect Octagon if 1 ≈ √2 (this being the highest accurate density low resolution (4X4), meaning solid numbers over the whole octagon). As far as it may be useful, I finally found the way to produce these numbers as coefficients from an algebraic equation as follows.
There are actually only four variables, in ratios, used to form the terms in this octagon. If the terms were left with variables each equal to 1, the coefficients will multiply to create these exact numbers.
N = 0



N = 1



N = 2



N = 3



N = 4



N = 5



N = 6



N = 7



N = 8



N = 9



N = 10



N = 11



N = 12



"...at any rate, a possibly harsh square knot of polynomials is in order at least. It looks beautifull and would make a quite nice connect the dots or coloring book."