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Talbot's Curve
Parametric Cartesian equation:
x
=
(
a
2
+
f
2
sin
2
(
t
)
)
cos
(
t
)
/
a
,
y
=
(
a
2
−
2
f
2
+
f
2
sin
2
(
t
)
)
sin
(
t
)
/
b
x = (a^{2} + f^{2}\sin^{2}(t))\cos(t)/a, y = (a^{2} - 2f^{2} + f^{2}\sin^{2}(t))\sin(t)/b
x
=
(
a
2
+
f
2
sin
2
(
t
)
)
cos
(
t
)
/
a
,
y
=
(
a
2
−
2
f
2
+
f
2
sin
2
(
t
)
)
sin
(
t
)
/
b
View the interactive version of this curve.
Description
This curve was investigated by
Talbot
.
Talbot
's curve is the negative pedal of an
ellipse
with respect to its centre. It has four cusps and two nodes provided the square of the eccentricity of the ellipse is greater than
1
2
\large\frac{1}{2}\normalsize
2
1
.
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
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