# What shape is a bean?

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
For some reason, this made me think of the shape from this question – mixedmath Dec 12 '12 at 7:36
It is bean-shaped. – Qiaochu Yuan Dec 12 '12 at 7:47
What kind of bean? There are a number of different types. – mike4ty4 Dec 12 '12 at 7:50
this seems to work for 2D $\quad r=\sin^3\theta+\cos^3\theta$ – Elements in Space Dec 12 '12 at 8:05