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Cardioid
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"∑ Back to Visual Dictionary Of Special Plane Curves .
Cardioid
Cardioid formed by its tangents
Mathematica Notebook for This Page ; cardioid_gallery.nb .
History
Studied by
Ole Roemer↗
(1674) in a investigation for the best form of gear teeth. The name cardioid (heart-shaped; from Greek root cardi, meaning heart) was first used by
de Castillon↗
in the Philosophical Transactions of the Royal Society of 1741. Its length is found by
Phillipe de la Hire↗
in 1708. Cardioid is a special case of limacon of Pascal : a family of curves studied and named after
Étienne Pascal↗
(1588-1640), father of Blaise Pascal↗ (1623-1662).
Description
Cardioid is a special case of epicycloid and limacon of Pascal . (see Curve Family Index )
Cardioid can be defined as the trace of a point on a circle that rolls around a fixed circle of the same size without slipping. Or, the trace of a point on a circle of radius 2 r that rolls inside a fixed circle of radius r. The latter is known as double generation. The figure on "
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