Superegg

A superegg or super-egg is a solid of revolution obtained by rotating an elongated super-ellipse with exponent greater than 2 around its longest axis. It is a special case of super-ellipsoid.

Unlike a elongated ellipsoid, an elongated superegg can stand upright on a flat surface, or on top of another superegg 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] . This is due to its curvature being zero at the tips.

The shape was popularized by Danish poet and scientist Piet Hein (1905–1996). Supereggs of various materials, like the one shown, were sold as novelties or "executive toys" in the 1960s. A 1-ton superegg made of steel and aluminum was placed outside Kelvin Hall in Glasgow in 1971, on occasion of a lecture by Piet Hein [ [http://www.daviddarling.info/encyclopedia/S/superegg.html "Superegg" in the Internet Encyclopedia of Science] ] .

Mathematical description

The superegg is a special case of a super-ellipsoid; it is defined by the implicit equation :$left|frac\{sqrt\{x^2\; +\; y^2\{r\}\; ight|^p\; +\; left|frac\{z\}\{h\}\; ight|^p\; leq\; 1$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 [ [http://www.matematiksider.dk/piethein.html Piet Heins Superellipse (in Danish)] ] .

References

ee also

* Egg of Columbus