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.