Kappa Curve

Cartesian equation:
y2(x2 + y2) = a2x2
Polar equation: r = a cot(θ)


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

If your browser can handle JAVA code, click HERE to experiment interactively with this curve and its associated curves.

The kappa curve is also called Gutschoven's curve. It was first studied by G. van Gutschoven around 1662.

The curve was studied by Newton and, some years later, by Johann Bernoulli.


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The URL of this page is:
http://www-history.mcs.st-andrews.ac.uk/Curves/Kappa.html