x(u, v) = cos(u) (sqrt(R^2 - v^2) - r) y(u, v) = sin(u) (sqrt(R^2 - v^2) - r) z(u, v) = v

(r^2 - R^2 + x^2 + y^2 + z^2)^2 = 4 r^2 (x^2 + y^2)

4

g = 0

S = 4 π R (R - r)

ds^2 = (r - sqrt(R^2 - v^2))^2 du^2 + v^2/(R^2 - v^2) dv^2

dA = (v (r - sqrt(R^2 - v^2)))/sqrt(R^2 - v^2) du dv

x^_ = (0, 0, 0)

V = 2/3 π (sqrt(R^2 - r^2) (r^2 + 2 R^2) - 3 r R^2 cot^(-1)(r/sqrt(R^2 - r^2)))

I = ((sqrt(R^2 - r^2) (2 r^4 + 101 r^2 R^2 + 32 R^4) - 15 r R^2 (4 r^2 + 5 R^2) cot^(-1)(r/sqrt(R^2 - r^2)))/(40 (sqrt(R^2 - r^2) (r^2 + 2 R^2) - 3 r R^2 cot^(-1)(r/sqrt(R^2 - r^2)))) | 0 | 0 0 | (sqrt(R^2 - r^2) (2 r^4 + 101 r^2 R^2 + 32 R^4) - 15 r R^2 (4 r^2 + 5 R^2) cot^(-1)(r/sqrt(R^2 - r^2)))/(40 (sqrt(R^2 - r^2) (r^2 + 2 R^2) - 3 r R^2 cot^(-1)(r/sqrt(R^2 - r^2)))) | 0 0 | 0 | (sqrt(R^2 - r^2) (6 r^4 + 83 r^2 R^2 + 16 R^4) - 15 r R^2 (4 r^2 + 3 R^2) cot^(-1)(r/sqrt(R^2 - r^2)))/(20 (sqrt(R^2 - r^2) (r^2 + 2 R^2) - 3 r R^2 cot^(-1)(r/sqrt(R^2 - r^2)))))

K(u, v) = (R^2 - v^2)/(R^2 (-r sqrt(R^2 - v^2) + R^2 - v^2))

E(u, v) = (r - sqrt(R^2 - v^2))^2 F(u, v) = 0 G(u, v) = v^2/(R^2 - v^2)

e(u, v) = -sqrt((R^2 - v^2) (r^2 - 2 r sqrt((R - v) (R + v)) + R^2 - v^2))/R f(u, v) = 0 g(u, v) = (R (r - sqrt(R^2 - v^2)))/((R^2 - v^2) sqrt(r^2 - 2 r sqrt(R^2 - v^2) + R^2 - v^2))

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