# Hypercylindrical Volume

americanforest
I'm a Physics major and my research mentor has given me a math assignment. He described what he wanted but, since I don't have any training in this area of math, I don't really know where to turn. I am supposed to find the volume of a shape that wraps around onto itself in n dimensions. I think of it as a cylinder. Anybody know where I can find information about this?

Crosson
Use the integration techniques from multivariable calc.

ObsessiveMathsFreak
Given the vaugeness of the question, I would be tempted to just integrate the volume parameterised by

$$S(r,\theta,z_1,z_2,\ldots,z_n) = (r\cos{\theta},r\sin{\theta},z_1,z_2,\ldots,z_n)$$

But I think the question you might have been asked was to find the volume of a hypersphere. That's easily googled. And has a few interesting properties as you move through the dimensions

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