Gielis’ Curves & Surfaces


In 1997 the superformula was discovered, which solved the problem of the limited symmetry of superellipses and supercircles. Supershapes like pentagons and starfish, triangles and rose sepals, flowers and leaves, can now be described by a single equation, based on the generalization of Lamé’s supercircles and superellipses.

The key step from Lamé’s supercircles was to convert the equations to polar coordinates and to add a single parameter for symmetry. It was extended into three dimensions as well.

This discovery was published in the book “Inventing the Circle” (2001, 2003) and as Invited Special Paper in the American Journal of Botany in April 2003. Worldwide awareness was created by websites such as Nature Science update, Science News Online, and Wolfram’s Mathematica website.

Supershapes were introduced later in the field of geometry under the general name of Gielis’ curves, surfaces & -transformations, also in higher dimensions.