||last updated: 2005-10-21
It was Gabriel (1795-1870) 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 y-directions. In
that case the symmetrical case has the name of super
circle (or supercircle).
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 (1905-1996) used the curve for architecture objects as motorway
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
- 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 y-axis:
Some examples are the following:
This curve has been generalized to the Gielis curve.
The three-dimensional version of the hyper ellipse has been called the super egg,
by Piet Hein.