A Singular Surface
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This animation depicts a standard surface from multivariable calculus.
(See notes below.)
The surface shown here is given by the equation
z = 2 x y ⁄ (x2 + y2), or, in
cylindrical coordinates, z = sin(2θ). Note that approaching the origin
along the ray θ = θ0 gives a limiting value of
z = sin(2θ0),
so that the surface cannot be continuous at the origin.
(11/27/07)