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Cayley's Sextic
Cartesian equation:
4
(
x
2
+
y
2
−
a
x
)
3
=
27
a
2
(
x
2
+
y
2
)
2
4(x^{2} + y^{2} - ax)^{3} = 27a^{2}(x^{2} + y^{2})^{2}
4
(
x
2
+
y
2
−
a
x
)
3
=
2
7
a
2
(
x
2
+
y
2
)
2
Polar equation:
r
=
4
a
cos
3
(
θ
/
3
)
r = 4a \cos^{3}( \theta /3)
r
=
4
a
cos
3
(
θ
/
3
)
View the interactive version of this curve.
Description
This was first discovered by
Maclaurin
but 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
.
The evolute of Cayley's Sextic is a
nephroid
curve.
Associated Curves
Definitions of the Associated curves
Evolute
Involute 1
Involute 2
Inverse curve wrt origin
Inverse wrt another circle
Pedal curve wrt origin
Pedal wrt another point
Negative pedal curve wrt origin
Negative pedal wrt another point
Caustic wrt horizontal rays
Caustic curve wrt another point