Shoe Surface
ShoeSurface
A surface given by the parametric equations
x(u,v) = u
(1)
y(u,v) = v
(2)
z(u,v) = 1/3u^3-1/2v^2.
(3)
The coefficients of the coefficients of the first fundamental form are
E = 1+u^4
(4)
F = -u^2v
(5)
G = 1+v^2,
(6)
and the second fundamental form coefficients are
giving area element
and Gaussian and mean curvatures
K = [画像:-(2u)/((1+u^4+v^2)^2)]
(11)
H = [画像:(2u(1+v^2)-u^4-1)/(2(1+u^4+v^2)^(3/2)).]
(12)
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References
Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, p. 965, 1997.Referenced on Wolfram|Alpha
Shoe SurfaceCite this as:
Weisstein, Eric W. "Shoe Surface." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ShoeSurface.html