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The Rose Curve

The Rose Curve. By Cailan Halliday And Sarah McCormick. History. Guido Grandi named this curve “rhodonea” or rose. What is the Rose Curve?. The petal of any hypocycloid or epicycloid What is a petal?. Period of the Rose Curve. r = cos(k θ ) Where k is a rational number Or

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The Rose Curve

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  1. The Rose Curve By Cailan Halliday And Sarah McCormick

  2. History • Guido Grandi named this curve “rhodonea” or rose

  3. What is the Rose Curve? • The petal of any hypocycloid or epicycloid • What is a petal?

  4. Period of the Rose Curve r = cos(kθ) Where k is a rational number Or r = cos(p/qθ) Where p and q are integers When p and q are both odd integers the period of the rose curve is π*q with p petals. Otherwise the period is 2*π*q and has 2*p petals If k is not a rational number (π, e, etc.) a solid disc will be drawn if θ is unbounded.

  5. Parameterization of the rose curve r = cos(p/q θ) x = rcos(θ) y = rsin(θ) ↓ x = cos(p/q θ)cos(θ) y = cos(p/q θ)sin(θ)

  6. Bibliography • Xah Lee, 1995-97 (5/8/06) http://xahlee.org/SpecialPlaneCurves_dir/specialPlaneCurves.html • Epitrochoids, Jan 1997 http://www-history.mcs.st-andrews.ac.uk/history/Curves.html • Roulette, rhodonea, 9 Aug 2005 (5/12/06) http://www.2dcurves.com/roulette/rouletter.html • Rose(mathematics), Wikipedia, 15 April 2006 (5/7/06) http://en.wikipedia.org/wiki/Rose_(mathematics) • Rose, Wolfram Research, Inc, 1999-2006 (5/7/06) http://mathworld.wolfram.com/Rose.html • Lockwood, E.H. 1967, A Book Of Curves, Cambridge University Press, New York

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