The epispiral is a plane curve with polar equation

An epispiral with equation r(θ)=2sec(2θ)

There are n sections if n is odd and 2n if n is even.

It is the polar or circle inversion of the rose curve.

In astronomy the epispiral is related to the equations that explain planets' orbits.

See alsoEdit


  • J. Dennis Lawrence (1972). A catalog of special plane curves. Dover Publications. p. 192. ISBN 0-486-60288-5.
  • https://www.mathcurve.com/courbes2d.gb/epi/epi.shtml