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How can I mathematically describe the shape of an idealised bean? (In two dimensions and in threes dimensions)

At the moment I'm calling the shape I refer to an ellipse/ellipsoid on a curved major axis.

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I bet you can make a cardoid look like a bean. – Alex Youcis Dec 12 '12 at 7:32
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For some reason, this made me think of the shape from this question – mixedmath Dec 12 '12 at 7:36
    
@Alex Youcis , A cardioid has a sharp indentation, a bean has a smooth indentation – Elements in Space Dec 12 '12 at 7:46
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It is bean-shaped. – Qiaochu Yuan Dec 12 '12 at 7:47
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What kind of bean? There are a number of different types. – mike4ty4 Dec 12 '12 at 7:50

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