Volume of intersection from multiple cylinders in higher dimensions

Asked Nov 26 '24 at 12:57

Active Nov 26 '24 at 13:28

Viewed 64 times

You can approximate the "Volume" of a 2D Sphere with a Cylinder (it is exact in 2D, both are circles/disks) For higher Dimensions, the calculation is just an rougher approximation.
In three dimensions with just two Cylinders:
Find the volume common to two circular cylinders, each with radius r, if the axes of the cylinders intersect at right angles. (using disk/washer)
But i Want N Cylinders in N Dimensions

Is there a similar easy formula fo the perpendicular intersection of N cylinders in N dimensions?

edited Nov 26 '24 at 13:28

asked Nov 26 '24 at 12:57

Jaroel

something like a steinmetz solid but with N cylinders in N dimensions – Jaroel Nov 26 '24 at 13:06
You can use the same solid-of-rotation integration method to go from $n-1$ dimension to $n$ dimensions for any $n>1$. – Paul Sinclair Nov 28 '24 at 22:16

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