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Harmonic Curves · 2D

Rhodonea Rose

r = cos(k·θ)

Rhodonea Rose, drawn as a glowing line figure

A curve with petals set by one ratio, k = n/d. Whole-number k gives a simple flower. Fractions weave overlapping petals into lace.

k
n / d

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Watch it drawn with compass and straightedge, hear the chord of its lines, and turn the Dimension dial to raise its form in space.

Facts

  • If k is an odd integer the rose has k petals; if even, 2k.
  • Fractions n/d give closed curves that take d full turns to complete.
  • Named by the 18th-century Italian mathematician Guido Grandi.

Across the dimensions

  • Shadow of Clelia CurveLet the rose’s radius be a circle of latitude: the curve winds over a sphere, and its shadow is the rose.

Learn it step by step

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