I know that, for k an integer, the rose polar curve expressed by r=r(θ)= cos(kθ) has a period of π if k is odd and 2π if k is even (usually expressed as saying that there are k distinct petals if k is odd, and 2k petals if k is even). However, I have yet to pin down the reason for this difference. Can anyone point out the reason (or calculations) for this conclusion? Thanks.(adsbygoogle = window.adsbygoogle || []).push({});

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# The domain of A for r=cos(kA) before the petals start to overlap

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