Curves96 of 113
Limaçon of Pascal
Albrecht Dürer, 1525; Étienne Pascal, 1630; named by Roberval, 1650
The curves r = b + a cos θ, drawn by a point fixed to a wheel, on or off its rim, as it rolls round a circle of the same size. With b less than a it has an inner loop; the loop shrinks to a cusp at b = a, the cardioid, then opens into a dimple that flattens away once b reaches 2a. It carries the name of Étienne Pascal, Blaise’s father, though Dürer had drawn it in 1525.
r = b + a cos θ
On mathcurve.com as Limaçon de Pascal
In the library
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Underweysung der Messung (Nuremberg, 1538)Albrecht Dürer1538, 1527, 1532Metropolitan Museum of Art, New York, NY Dürer’s treatise gives geometric methods for drawing limaçons. The page reproduced here is not one of them: it shows column bases and ornamental outlines.
Not yet checkedSuggested by an AI model, 2026-10-09Source
An AI reviewer agreed, 2026-10-09: The source page states "Dürer's Underweysung der Messung (Instruction in Measurement) contains specific geometric methods for producing limaçons." This supports the claim about the work. The picture matches the note's admission that this page is not one of those methods, since it shows stepped column profiles with bases on the left and lobed ornamental outlines on the right.