epi spiral


last updated: 20041204 
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.
