Consider the unit hypersphere (with radius r = 1). Inside the hypersphere inscribe a hypercube (i.e., the
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Question:
(a) Derive an expression for the volume of the inscribed hypercube for any given dimensionality d. Derive the expression for one, two, and three dimensions, and then generalize to higher dimensions.
(b) What happens to the ratio of the volume of the inscribed hypercube to the volume of the enclosing hypersphere as d → ∞? Again, give the ratio in one, two and three dimensions, and then generalize.
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