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Lamé curve
Any of a family of curves related to the ellipse and that was first recognized and studied in 1818 by the French physicist and mathematician Gabriel Lamé (1795-1870). The formula for the Lamé curve family is a generalization of the equation for an ellipse (|x/a|2 + |y/b|2 = 1), namely:
where n is any real number.
When n = 0, the curve reduces to a pair of crossed lines. As n increases, the curve changes from a curved star shape to a rectangle, with diagonals a and b, when n = 1. The special case when n = 2/3 corresponds to the astroid. Between n = 1 and n = 2 the curve turns from a curved rectangle to an ellipse (or a circle when both a and b are 1). For values of n greater than 2, Lamé curves are known as superellipses.
Related category
• PLANE CURVES
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