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

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, pp. 223-224, 1987.

Hall, L. "Trochoids, Roses, and Thorns--Beyond the Spirograph." College Math. J. 23, 20-35, 1992.

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 175-177, 1972.

MacTutor History of Mathematics Archive. "Rhodonea Curves." http://www-groups.dcs.st-and.ac.uk/~history/Curves/Rhodonea.html.

Wagon, S. "Roses." §4.1 in Mathematica in Action. New York: W. H. Freeman, pp. 96-102, 1991.

CITE THIS AS:

Weisstein, Eric W. "Rose." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Rose.html