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Curves

Quadratrix of Hippias

Main
Cartesian equation:
y=xcot⁡(πx/2a)y = x \cot(πx/2a)
Polar equation:
r=2aθ/(πsin⁡(θ))r = 2a \theta /(π\sin( \theta ))

View the interactive version of this curve.

Description

The quadratrix was discovered by Hippias of Elis in 430 BC. It may have been used by him for trisecting an angle and squaring the circle. The curve may be used for dividing an angle into any number of equal parts.

Later it was studied by Dinostratus in 350 BC who used the curve to square the circle.

Hippias of Elis was a statesman and philosopher who travelled from place to place taking money for his services. Plato describes him as a vain man being both arrogant and boastful. He had a wide but superficial knowledge. His only contribution to mathematics seems to be the quadratrix.

Other Web sites:

Xah Lee
M D Huberty

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