epi spiral


last updated: 2004-12-04

For a being integer, the curve is more radial compound hyperbola, than a spiral. The number of sections depends on the value of the parameter a: for odd a there are 'a' sections, for even 'a' there are 2a sections.

For a=2, we see the cross curve.
For a=3, the curve is the trefoil

Non integer values for a give the curve the spiral form.
For a=1/3, we see the trisectrix of MacLaurin.
For a=1/2 the curve has the name of trisectrix of Delange.





The epi spiral is a special case of the Cotes' spiral.
And the curve is the polar inverse of the rhodonea.

The curves were studied in 1895 by Aubry.