A plane curve discovered by Maclaurin but first studied in detail by Cayley. The name Cayley's sextic is due to R. C. Archibald, who attempted to classify curves in a paper published in Strasbourg in 1900 (MacTutor Archive). Cayley's sextic is given in polar coordinates by
(1)
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The Cartesian equation is
(2)
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Parametric equations can be given by
(3)
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(4)
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for . In this parametrization, the loop corresponds to .
The area enclosed by the outer boundary is
(5)
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(6)
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(OEIS A118308), and by the inner loop is
(7)
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(8)
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(OEIS A118309), and the arc length of the entire curve is
(9)
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The arc length, curvature, and tangential angle are given by
(10)
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(11)
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(12)
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