Editing Polar coordinate system (section)

===Polar rose===
[[Image:Rose 2sin(4theta).svg|thumb|right|A polar rose with equation {{math|1=''r''(''φ'') {{=}} 2 sin 4''φ''}}]]
A [[rose (mathematics)|polar rose]] is a mathematical curve that looks like a petaled flower, and that can be expressed as a simple polar equation,
<math display="block">r(\varphi) = a\cos\left(k\varphi + \gamma_0\right)</math>

for any constant γ<sub>0</sub> (including 0). If ''k'' is an integer, these equations will produce a ''k''-petaled rose if ''k'' is [[even and odd numbers|odd]], or a 2''k''-petaled rose if ''k'' is even. If ''k'' is rational, but not an integer, a rose-like shape may form but with overlapping petals. Note that these equations never define a rose with 2, 6, 10, 14, etc. petals. The [[variable (math)|variable]] ''a'' directly represents the length or amplitude of the petals of the rose, while ''k'' relates to their spatial frequency. The constant γ<sub>0</sub> can be regarded as a phase angle.
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