Shreyas' blog – Ignited Minds

1. Introduction The first installment of this post investigated the question of computing the volume of a unit ball (and by extension any ball) of dimensions. The main result we obtained was that the volume can be computed recursively as , where     In this post, we will use this result to prove an explicit formula for . 2. The Formula A quick search online yields the following explicit formula for :     where the function extends the…

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1. Introduction This post investigates an interesting question I had been thinking about: we all know that the area of a circle of radius equals , and the volume of a sphere of radius equals . But what if we enter the territory of even higher dimensions? We should be able to say something about the “volume” of an n-dimensional sphere, where “volume” is interpreted as the equivalent measure of space in that many dimensions (e.g. area for 2D, regular…

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