MacTutor logo MacTutor

Curves

Kampyle of Eudoxus

Main
Cartesian equation:
a2x4=b4(x2+y2)a^{2}x^{4} = b^{4}(x^{2} + y^{2})
Polar equation:
r=b2/(acos⁡2(θ))r = b^{2}/(a \cos^{2}( \theta ))

View the interactive version of this curve.

Description

A curve studied by Eudoxus also in relation to the classical problem of duplication of the cube.

Eudoxus was a pupil of Plato. His main work was in astronomy. He was the first to describe the constellations and invented the astrolabe. He introduced the study of mathematical astronomy into Greece.

Eudoxus found formulas for measuring pyramids cones and cylinders. His work contains elements of the calculus with a rigorous study of the method of exhaustion.

The word kampyle comes from the Greek καμπύλη meaning curve.

Further information:

J H McCoy

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