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| [[Image:Superaeg.jpg|right|thumb|Brass superegg by [[Piet Hein (Denmark)|Piet Hein]].]]
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| In [[geometry]], a '''superegg''' is a [[solid of revolution]] obtained by rotating an elongated [[superellipse|super-ellipse]] with [[exponentiation|exponent]] greater than 2 around its longest axis. It is a special case of [[superellipsoid|super-ellipsoid]].
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| Unlike an [[prolate spheroid|elongated ellipsoid]], an elongated superegg can stand upright on a flat surface, or on top of another superegg.<ref name=gardner>{{cite book | last=Gardner | first=Martin | author-link=Martin Gardner | chapter=Piet Hein’s Superellipse | year=1977 | title=Mathematical Carnival. A New Round-Up of Tantalizers and Puzzles from Scientific American | location=New York | publisher=[[Vintage Press]] | pages=240–254 | isbn=978-0-394-72349-5}}</ref> This is due to its [[curvature]] being zero at the tips.
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| The shape was popularized by Danish poet and scientist [[Piet Hein (Denmark)|Piet Hein]] (1905–1996). Supereggs of various materials, like the one shown, were sold as novelties or "[[executive toy]]s" in the 1960s. A 1-ton superegg made of [[steel]] and [[aluminium]] was placed outside [[Kelvin Hall]] in [[Glasgow]] in 1971, on occasion of a lecture by Piet Hein.<ref>[http://www.daviddarling.info/encyclopedia/S/superegg.html "Superegg" in the Internet Encyclopedia of Science]</ref>
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| ==Mathematical description==
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| The superegg is a super-ellipsoid whose horizontal cross-sections are circles. It is defined by the [[implicit function|implicit equation]]
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| :<math>\left|\frac{\sqrt{x^2 + y^2}}{r}\right|^p + \left|\frac{z}{h}\right|^p \leq 1</math>
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| where ''r'' is the horizontal radius at the "equator" (the widest part), and ''h'' is one half of the height. The [[exponent]] ''p'' determines the degree of flattening at the tips and equator. Hein's choice was ''p''=2.5 (the same he used for the [[Sergels Torg]] roundabout), and ''r''/''h'' = 3/4.<ref>[http://www.matematiksider.dk/piethein.html Piet Heins Superellipse (in Danish)]</ref>
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| The definition can be changed to have a strict equality rather than inequality, this changes the superegg to being a [[surface of revolution]] rather than a solid.<ref>[[Eric W. Weisstein|Weisstein, Eric W]]. "Superegg." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Superegg.html</ref>
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| ==See also==
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| * [[Egg of Columbus]]
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| {{Portal bar|Denmark|Mathematics|Toys}}
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| ==References==
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| {{Reflist}}
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| [[Category:Algebraic curves]]
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| [[Category:Surfaces]]
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| [[Category:Executive toys]]
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| {{Geometry-stub}}
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