I just looked at the link you referenced. No, Poncelet's Porism (interesting though it may be) appears to involve n-gon sides which _aren't_ of equal length. I'm looking for n-gons with all n sides equal whose vertices all lie on an ellipse (i.e., the ellipse circumscribes the n-gon). At 08:51 PM 11/17/2010, Victor Miller wrote:

Is what you want related to Poncelet's Porism? http://mathworld.wolfram.com/PonceletsPorism.html

On Wed, Nov 17, 2010 at 11:39 PM, Henry Baker <hbaker1@pipeline.com> wrote:

...

In playing with the Marden Theorem, I started thinking about approximations to ellipses, and was wondering about regular elliptical n-gons. I'm not talking about a regular n-gon stretched/squashed or squashed in the X or Y direction, because for stretched/squashed n-gons the lengths of those sides are no longer equal.

Since the perimeter of an ellipse isn't easily calculated, I would imagine that this will be a difficult problem.

What I'm really looking for is a kind of inverse to the ellipse perimeter problem: given n sides of length 1 and a major/minor radius ratio (alternately an eccentricity), how to draw the ellipse itself. Which major/minor ratios and/or eccentricities can actually be represented this way?

I would assume that someone has looked into this sort of problem, but I wouldn't even know where to begin to look.