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    Hypersphere

    Equation

    sum_(i=1)^n x_i^2 = r^2 (assuming embedding dimension n and radius r)

    Properties

    diameter | 2 r content | (2 π^(n/2) r^n)/(n Γ(n/2))≈(2 3.14159^(0.5 n) r^n)/(n Γ(0.5 n)) hyper-surface area | (2 π^(n/2) r^(n - 1))/Γ(n/2)≈(2 3.14159^(0.5 n) r^(n - 1))/Γ(0.5 n) (assuming embedding dimension n and radius r)

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