Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I don't know much about calculus of variation, but I think it applies to a problem I've come across. If you have a closed loop in a 2 dimensional space defined by some parametric equation r(t), is there some minimization or maximization of parameters, like arc length or enclosed area, that will yield a family of ellipses as the solution?

I'm asking because a professor showed me an iterative process that seems to take any randomly generated polygon and by averaging the lengths of the edges, somehow "untangles" the polygon and over many iterations the shape converges to an ellipse. They had no proof for the convergence to the ellipse. I was wondering if it could be approached as a discretization of some continuous minimization process.

share|improve this question
    
Two characterizations that might lead to a variational problem for which families of ellipses are the solution are (i) the pins-and-strings locus and (ii) the image of the unit circle under a linear transformation. Do you recall any more about the iterative "averaging" process? –  anon Mar 1 '12 at 2:02
add comment

Know someone who can answer? Share a link to this question via email, Google+, Twitter, or Facebook.

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.