Mathematica 9 is now available

Wolfram Library Archive

Courseware Demos MathSource Technical Notes
All Collections Articles Books Conference Proceedings

Trochoids, Roses, and Thorns--Beyond the Spirograph

Leon Hall
Journal / Anthology

The College Mathematics Journal
Year: 1992
Volume: 23
Issue: 1
Page range: 20-35

Horticulturally, roses and thorns go together. Mathematically, roses, along with other curves having interesting names, are encountered in connection with polar coordinates, but thorns are not mentioned. Perhaps this is because mathematical roses do not have stems, or maybe mathematicians have been unwilling to push the floral nomenclature too far. Sometimes mathematical objects get named in roundabout ways, but in this paper, regardless of tradition, "petals" will be used instead of "leaves" when describing roselike curves. As for the thorns, we shall see that there are indeed curves with a definite thorny appearance that are closely related to mathematical roses.

*Mathematics > Geometry > Plane Geometry