Superellipse

A curve of the form

$$\left\vert{x\over a}\right\vert^r+\left\vert{y\over b}\right\vert^r=1.$$

where $r>2$. ``The'' superellipse is sometimes taken as the curve of the above form with $r=5/2$. Superellipses with $a=b$ are also known as Lamé Curves. The above curves are for $a=1$, $b=2$, and $r=2.5$, 3.0, and 3.5.

A degenerate superellipse is a superellipse with $r\leq 2$. The above curves are for $a=1$, $b=2$, and $r=0.5$, 1.0, 1.5, and 2.0.

See also Ellipse, Lamé Curve, Superegg

References

Gardner, M. ``Piet Hein's Superellipse.'' Ch. 18 in Mathematical Carnival: A New Round-Up of Tantalizers and Puzzles from Scientific American. New York: Vintage, 1977.