The discovery of supercircles and superellipses allow us to look beyond circle and lines. To quote Piet Hein: “The superellipse has the same beautiful unity as circle and square, but is less obvious and less plane. The superellipse frees us from the straightjacket of simpler curves such as lines and planes.”
Supercircles are defined by an equation in which only one parameter, the exponent, is sufficient to identify circles, squares or any intermediate shape. As a consequence, the slightest deviations of circle and square can be understood simply as slight changes of the exponents in the equations.
This is also important during growth and development. The circle is considered as the perfect shape, but in reality it is not important if a shape is not precisely a circle; a supercircle is just a good. Many cells, organs or plant stems, develop according to their own supercircle.While many square shapes are found in nature, one finds triangles, pentagons and hexagons much more often than squares. A prime example is a starfish. These shapes cannot be described as supercircles that are limited to squares or rectangles.