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Superegg

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Superegg

A superegg is a solid described by the equation

|sqrt((x^2+y^2)/(a^2))|^n+|z/b|^n=1.
(1)

The special case n=2 gives a spheroid.

Supereggs and their planar generating curves are studied in squigonometry (Poodiack 2016).

Special cases of volume V_n are given by

V_1=2/3pia^2b
(2)
V_2=4/3pia^2b.
(3)

See also

Capsule, Egg, Oblate Spheroid, Prolate Spheroid, Spheroid, Squigonometry, Superellipse, Superellipsoid, Supersphere

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References

Bourke, P. "Superellipse and Superellipsoid: A Geometric Primitive for Computer Aided Design." http://astronomy.swin.edu.au/~pbourke/surfaces/superellipse/.Gardner, M. "Piet Hein's Superellipse." Ch. 18 in Mathematical Carnival: A New Round-Up of Tantalizers and Puzzles from Scientific American. New York: Vintage, pp. 240-254, 1977.Poodiack, R. D. "Squigonometry, Hyperellipses, and Supereggs." Math. Mag. 89, 92-102, 2016. https://doi.org/10.4169/math.mag.89.2.92.Vestergaard, E. "Piet Heins Superellipse." https://www.matematiksider.dk/piethein.html.

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Superegg

Cite this as:

Weisstein, Eric W. "Superegg." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Superegg.html

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