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Curves

Hyperbolic Spiral

Main
Polar equation:
r=a/θr = a/ \theta

View the interactive version of this curve.

Description

The hyperbolic spiral originated with Pierre Varignon in 1704. It was studied by Johann Bernoulli between 1710 and 1713 and it was also studied by Cotes in 1722.

The roulette of the pole of a hyperbolic spiral rolling on a straight line is a tractrix.

Pierre Varignon (1654-1722) was professor of mathematics at Collège Mazarin and later at Collège Royal. Led into mathematics by reading Euclid he also read Descartes' Géométrieand thereafter devoted himself to the mathematical sciences. He was one of the first French scholars to recognise the value of the calculus. His chief contributions were to mechanics.

Taking the pole as the centre of inversion, the hyperbolic spiral r = a/θ inverts to the spiral of Archimedes r = aθ.

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