I guess one way to inscribe an equilateral n-gon in an ellipse of semimajor axis a and semiminor axis b would be to start with the 4 points (a,0), (0,b), (-a,0), (0,-b) forming a diamond inscribed in the ellipse, and then recursively constructing a little triangle on each of these diagonals which intersects the ellipse. In this way, we can construct an equilateral 2^n-gon within the ellipse. I assume that calculating the point of intersection of the perpendicular bisector of an existing side with the ellipse is the solution of a polynomial equation ?? At 06:47 AM 11/18/2010, Henry Baker wrote:

I was looking for an equi _lateral_ n-gon inscribed in an ellipse. It is more important that the (straight line segment) sides be equal, than that the vertices occur at equal curve segments around the edge. In an ellipse, it won't be possible to do both at the same time.

At 06:40 AM 11/18/2010, Michael Kleber wrote:

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Wait, Henry, do you really mean you want "equal spacing along the perimeter of the ellipse"? I thought you wanted equal side lengths, and didn't care about the length of the ellipse arc they subtended.

--Michael

On Thu, Nov 18, 2010 at 9:30 AM, Henry Baker <hbaker1@pipeline.com> wrote:

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I think that by using the term "regular" instead of "equilateral", I confused everyone.

I'm trying to find a simple way to generate n-vertex equilateral ellipses. It is particularly important for the application I have in mind that the vertices are at equal spacing along the perimeter of the ellipse, and most importantly, that the sequence closes after one trip around -- i.e., there can't be any gap.

The reason is that I want to use these little vectors as accelerations, and if they don't sum up exactly to zero, then the velocities & positions don't have any hope of closing up.