super ellipse


last updated: 20051021 
It was Gabriel (17951870) who was the first to study this class of curves (in 1818),
leading to the name of Lamé curve.
The curve can be seen as a generalisation of an ellipse,
a super ellipse (or superellipse). Sometimes the name of super
ellipse is only used when the curve is equal in both x and ydirections. In
that case the symmetrical case has the name of super
circle (or supercircle).
For
a < 2, the curve is also named a hypoellipse.
A circle goes via a square (a = 1) in the
direction of a cross (a = 0).
A special case is the astroid, for a =
2/3. Some authors call the general case the astroid.
a = 2 gives the cross curve.
For a > 2, the curve is also named a hyperellipse.
A special case is Piet Hein's ellipse,
for a = 5/2. This
Danish poet and architect (19051996) used the curve for architecture objects as motorway
bridges.
The Melior font, designed by Hermann Zapf (in 1952), was based on this curve.
Super ellipse have also been used for:
 a roundabout in an old city square Sergels Torg in Stockholm, Sweden
 a table for the Vietnam War negotiators in Paris, 1969. The story is that
Piet Hein helped the parties agree on the shape for the negotiating
table
 the Azteca Olympic Stadium in Mexico City, Mexico (1968)
The curve can be extended to the generalized
super ellipse, removing the symmetry between x and yaxis:
Some examples are the following:
This curve has been generalized to the Gielis curve.
The threedimensional version of the hyper ellipse has been called the super egg,
by Piet Hein.
