In mathematics, limaçons, also known as limaçons of Pascal (pronounced with a soft c), are heart-shaped mathematical curves. The cardioid is a special case, with a cusp.

They arise in polar coordinates in the form

and

The term derives from the Latin word limax which means "snail".

History

Formal research on limaçons is attributed to Étienne Pascal , father of Blaise Pascal. However investigations began earlier by the German Renaissance artist, Albrecht Dürer. Dürer's Underweysung der Messung (Instruction in Measurement) [1], contains specific geometric methods for producing limaçons.

Visualizations