Talbot's Curve

Cartesian equation: x = (a^2+f^2sin^2(t))cos(t)/a, y = (a^2-2f^2+f^2sin^2(t))sin(t)/b

Click below to see one of the 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
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.

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JOC/EFR February 1996