## nephroid
Traité de la lumière (1690). A physical explanation wasn't forthcoming,
however, until 1838 when George Airy gave a
proof in terms of the wave theory of light. The name "nephroid" (from the Latin for "kidney-shaped") was introduced in 1878 by the English mathematician Richard Proctor in his book The Geometry of Cycloids. Prior to that it was known
as a two-cusped epicycloid. Specifically, the nephroid is the epicycloid formed by a circle of radius a rolling
around the outside on a fixed circle of radius 2a. It has a length
of 24a, an area of 12π^{2}, and is given by the parametric
equations: x = a(3cos t - 3cos 3t)y = a(3sin t - sin 3t). The nephroid is the involute of Cayley's sextic and is also the envelope of circles with their centers on a given circle, touching a given diameter of that circle. ## Freeth's nephroidThe nephroid has been described as the perfect shape for a multi-seat dining table. Not to be mistaken with the ordinary nephroid, just described, isFreeth's nephroid, named after the English mathematician
T. J. Freeth (1819–1904) who first wrote about it in a paper published
by the London Mathematical Society in 1879. Freeth's nephroid is the strophoid of a circle and has the polar equation r = a(1 + 2sinθ/2).
Freeth's nephroid is also the name of group of mathematicians, mostly from
Royal Holloway College, London, who gather weekly in a pub called the Beehive
and compete in games of trivial pursuit.## Related category• PLANE CURVES | |||||||

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