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Trochoids, Roses, and Thorns--Beyond the Spirograph
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| The College Mathematics Journal |
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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.
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