geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

, a superegg is a solid of revolution obtained by rotating an elongated superellipse with exponent greater than 2 around its longest axis. It is a special case of

superellipsoid In mathematics, a superellipsoid (or super-ellipsoid) is a solid whose horizontal sections are superellipses (Lamé curves) with the same exponent ''r'', and whose vertical sections through the center are superellipses with the same exponent '' ...

. Unlike an elongated ellipsoid, an elongated superegg can stand upright on a flat surface, or on top of another superegg. 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, including brass, were sold as novelties or "

executive toy An office toy (also known as an executive toy or a desk toy) is a novelty item typically placed on the desk of a corporate executive or other office worker. They have no work-related function, but are often intended to provide decoration or ple ...

s" in the 1960s.

Mathematical description

The superegg is a superellipsoid whose horizontal cross-sections are circles. It is defined by the inequality :

\left, \frac\^p + \left, \frac\^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 one he used for the

Sergels Torg Sergels torg ("Sergel's Square") is a major public square in Stockholm, Sweden, constructed in the 1960s and named after 18th-century sculptor Johan Tobias Sergel, whose workshop was once located north of the square. Overview Sergels torg ha ...

roundabout), and ''R''/''h'' = 3/4. The definition can be changed to have an equality rather than an inequality; this changes the superegg to being a

surface of revolution A surface of revolution is a surface in Euclidean space created by rotating a curve (the generatrix) around an axis of rotation. Examples of surfaces of revolution generated by a straight line are cylindrical and conical surfaces depending on ...

rather than a solid. Weisstein, Eric W. "Superegg." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Superegg.html

References

Algebraic curves Surfaces Executive toys Educational toys {{Geometry-stub

Mathematical description

See also

References