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https://www.psychforums.com/blog/highdimensionman/ncubing_the_nsphere_helpful_insights._b-14003_sid-951e1a9d589f93fd56ca0b1019988e95.html |
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| Author: | highdimensionman [ Tue Oct 05, 2021 7:53 pm ] |
| Blog Subject: | N-Cubing the N-Sphere helpful insights. |
Function one. As you move from first a straight line to a diagonal of the line crossing through a circle as the corners from a straight line to now a rectangle approach a square corner and then as the square becomes a cube and the circle becomes a sphere. Function one is a function which can produce the triangle ratios and angles produced from such a line intersecting an N-Sphere as it goes up dimension. Function two. If I can produce an efficient function one I would like to produce from that a function which calculates the ratio volume difference between an N-cube and an N-sphere. Function three. After this I would like to find a fast way to produce logarithms based on N-sphere volume as it goes up dimension. If I can't get off the ground there are a few things that can be done with current maths. NSphere to N-Cube ratios could be published which could speed up N-sphere calculations and mean a lot less code input. At least up to 3 dimensions probably 4 or higher could be explored as to the mass of n-spheres relative to real number dimensions and hence a bit of logarithmics. |
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