Kappa Curve

Cartesian equation: y^2(x^2+y^2) = a^2x^2

Polar equation: r = a cot(theta)

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
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.

Welcome page                         Famous curves index

Previous curve       (Famous curves)          Next curve

Biographical Index                          Chronologies

History Topics Index                      Birthplace Map

Mathematicians of the day     Anniversaries for the year

Search Form     Simple Search Form    Search Suggestions
JOC/EFR February 1996