Cayley's Sextic Evolute
CayleysSexticEvolute
The evolute of Cayley's sextic with parametrization
x = 4acos^3(1/3theta)cost
(1)
y = 4acos^3(1/3theta)sint
(2)
is given by
x_e = 1/4[2+3cos(2/3t)-cos(2t)]
(3)
y_e = sin^3(2/3t).
(4)
With parametrization
x = 4acos^4(1/2t)(2cost-1)
(5)
y = 4acos^3(1/2t)sin(3/2t),
(6)
the evolute is given by
x_e = 1/4[2+3cost-cos(3t)]
(7)
y_e = sin^3t.
(8)
This curve is a nephroid.
See also
Cayley's Sextic, Evolute, NephroidExplore with Wolfram|Alpha
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Cite this as:
Weisstein, Eric W. "Cayley's Sextic Evolute." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CayleysSexticEvolute.html