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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
- <math>r = a + b \sin \theta \ <math>
and
- <math>r = a + b \cos \theta \ <math>
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] (http://www.octavo.com/collections/projects/duruwm/), contains specific geometric methods for producing limaçons.
Visualizations
Missing image
Limacons.png
Image:limacons.png
de:Pascalsche Schnecke
it:Chiocciola di Pascal