8
$\begingroup$

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.


EDIT

This seems to work for 2D: $$r \leq \sin^3\theta+\cos^3\theta$$

bean

  • 0
    I bet you can make a cardoid look like a bean.2012-12-12
  • 1
    For some reason, this made me think of the shape from this [question](http://math.stackexchange.com/q/70320/9754)2012-12-12
  • 0
    @Alex Youcis , A cardioid has a sharp indentation, a bean has a smooth indentation2012-12-12
  • 6
    It is bean-shaped.2012-12-12
  • 3
    What kind of bean? There are a number of different types.2012-12-12
  • 0
    Claim to fame: we should come up with one. In the spirit of the paraboloid and ellipsoid, I propose the legumenoid. Edit: Oh, we're not actually naming this thing. Oops. Well it's homeomorphic to the unit ball, should we describe via homeomorphism?2012-12-12
  • 0
    It would be a surface homeomorphic to the ball with a saddle point? Would that be sufficient to characterize it?2012-12-12
  • 0
    @Alex: I see that beans are close to your heart... :-)2012-12-12
  • 3
    this seems to work for 2D $\quad r=\sin^3\theta+\cos^3\theta$2012-12-12
  • 0
    I am not sure how to get the 3D curve.2013-01-01
  • 0
    What does bean-shaped mean @QiaochuYuan?2013-01-11
  • 0
    Four years later., just curious... did you ever get your 3D, kidney-shaped bean?2017-07-03
  • 0
    Nope. I can't work out how to revolve it around a curved axis.2018-05-14

1 Answers 1