Recently I've been studying the the volume of an n-ball. Do hyperspheres (or their volume/surface formulas) have any real-world applications?
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1$\begingroup$ You might just want to calculate integrals in dimension higher than $3$ occasionally. $\endgroup$– user239203Commented Aug 18, 2019 at 16:23
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$\begingroup$ Do you mean some generalization of volume integrals? How could that be related to hyperspheres? $\endgroup$– Tu1Commented Aug 18, 2019 at 17:04
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$\begingroup$ Why so many downvotes? Was that a stupid question — like they clearly have no application at all? $\endgroup$– Tu1Commented Aug 18, 2019 at 18:54
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1$\begingroup$ I don't know why the downvotes. The fact is that if you want to put a measure on $\Bbb R^n$ (which is a generalization of the concept of "volume"), then knowing the measure of a ball is something that you'd somehow expect to know. $\endgroup$– user239203Commented Aug 18, 2019 at 19:42
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I don't think this question deserves any downvotes as it is a legitimate question regarding mathematics. An actual answer to your question, I believe that multiple dimensions are like number theory in a way, while they may not be physically present in real life, they are interesting topics that may help us to discover new things. Hyperspheres (multiple dimensions in general) open up a new world of both mathematics and physics where the idea that we do not live in just the three dimensions we can see takes place. For example, string theory is one currently unproven theory that may or may not be correct, stating that many more dimensions exist, but they are too small for any life to observe.
