The ding-dong surface is the cubic surface
of revolution given by the equation

(1)

(Hauser 2003) that is closely related to the kiss surface .

The surface can be represented in parametric form as

for
and .
In this parametrization, the coefficients of the first
fundamental form are

and of the second fundamental form are

The Gaussian and mean
curvatures are given by

The Gaussian curvature can be given implicitly by

(13)

The surface area and volume
enclosed by the upper teardrop are

It has centroid at ,
and moment of inertia tensor

(16)

for a solid teardrop with uniform density and mass .

See also Cubic Surface ,

Kiss Surface ,

Pear-Shaped Curve ,

Teardrop
Curve
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References Hauser, H. "Gallery of Singular Algebraic Surfaces: Dingdong." https://homepage.univie.ac.at/herwig.hauser/gallery.html . Hauser,
H. "The Hironaka Theorem on Resolution of Singularities (Or: A Proof We Always
Wanted to Understand)." Bull. Amer. Math. Soc. 40 , 323-403, 2003.
Cite this as:
Weisstein, Eric W. "Ding-Dong Surface."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/Ding-DongSurface.html

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