botanic curve


last updated: 20041204 
The botanic curve is the conchoid
of the rhodonea.
Its name is derived from her petallike form.
Other names for the curve are:
The following qualities of the rhodonea hold also for the botanic curve:
 the
number of petals is the denominator of 1/2  1/(2c)
 for integer values for c the number of petals is c (c odd), or 2c (c even)
 when c is irrational the curve does not close, and the number of petals is
infinite
 when the parameter c is rational, the resulting curve is algebraic
The following botanic curves have been given a special name:
Some examples for other values of c:
You can observe that the value of d defines the form of the petals: for d
< 1 the petal is open, it closes for d=1 and it forms an extra small petal
for d>1. John Baines made a Flash
script to produce the curve. 