I am trying to approximate the volume higher order unity spheres by using finitely small higher order cubes. (using python)
It is obvious that this is related to integrating by approximation by putting some finitely small cubes, but I am not able to figure out how to put the integration limits, I have even tried to imitate the method used to derive the volume of a 3d sphere but it did not work in this case since the rule to calculate the area is much more complicated.
I am aware of the rules to calculate the volume and area of higher order spheres and cubes, the codes to approximate integration such as the triangle and trapeze rules and even the monte carlo integration(which should not be used in this case). But I am still stuck, although this does not seem as a very complicated problem.
Any hint would be more than appreciated
https://en.wikipedia.org/wiki/N-sphere#Volume_and_surface_area