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Rose (mathematics)

From Biocrawler, the free encyclopedia.

In mathematics, a rose is a sinusoid plotted in polar coordinates. Up to similarity,

$\!\,r=cos(k\theta)$

One obtains a rose-like graph with $2 k$ petals if $k$ is even and $k$ petals if $k$ is odd. Assuming you use the given form, the whole rose will appear inside a unit circle. Using sine instead of cosine, and vice versa, the graphs differ by a rotation of $\frac{\pi}{2}$ radians—or that $\sin(kt + \frac{\pi}{2}) = \cos(kt)$ , and the graphs coincide.

More interesting results arise when $k$ is a rational. If $k$ is irrational, without bounds on $\,\!\theta$ , a disc results. In more detail, if $k$ is irrational, the number of petals is irrational, and the only thing preventing you from a solid-appearing disc is the upper limit on $\,\!\theta$ . Assuming a $k$ of $π$ , a $\,\!\theta$ limit of 2520 degrees (14 $π$ radians) will give you the first complete circle.

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External links

Mathworld article on rose curves (http://mathworld.wolfram.com/Rose.html)

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