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 In geometry, a solid of revolution is a solid figure obtained by rotating a plane figure around some straight line (the ''axis of revolution'') that lies on the same plane. The surface created by this revolution and which bounds the solid is ...

obtained by rotating an elongated

superellipse A superellipse, also known as a Lamé curve after Gabriel Lamé, is a closed curve resembling the ellipse, retaining the geometric features of semi-major axis and semi-minor axis, and symmetry about them, but a different overall shape. In the ...

with

exponent Exponentiation is a mathematical operation, written as , involving two numbers, the '' base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". When is a positive integer, exponentiation corresponds to re ...

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 In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane. For curves, the cano ...

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 toys" 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

''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 h ...

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 w ...

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