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A sphere is the nicest surface with constant Gaussian curvature κ=1, but these surfaces also have κ=1, except at the cusps. In cylindrical coords: z = √(1-χ²) E(arcsin(ρ/χ) | χ²/(χ²-1)) z is measured from a cusp χ is radius of equator E is an elliptic integral of the 2nd kind | Applications Of Mathematics
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