Rose
A curve which has the shape of a petalled flower. This curve was named rhodonea by the Italian mathematician Guido Grandi between 1723 and 1728 because it resembles a rose (MacTutor Archive). The polar equation of the rose is
 |
or
 |
If 
is odd, the rose
is 
-petalled. If 
is even,
the rose is 
-petalled.
If 
is a rational
number, then the curve closes at a polar angle of 
, where
if 
is odd and 
if 
is even.
If 
is irrational,
then there are an infinite number of petals.
The following table summarizes special names gives to roses with various values of 
.
 | curve |
| 2 | quadrifolium |
| 3 | trifolium, paquerette de mélibée |
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rose
