I don't have a proof. Yet, I suspect that the maximum perimeter is given by a^2 + b^2 + sqrt(a^4 - (ab)^2 + b^4) 2 sqrt(3) -------------------------------------------- sqrt(a^2 + b^2 + 2 sqrt(a^4 - (ab)^2 + b^4)) where a and b are the lengths of the semiaxes of the ellipse. David ----- Original Message ----- From: "Dan Asimov" <dasimov@earthlink.net> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Friday, September 07, 2007 21:24 Subject: [math-fun] Puzzle re maximum perimeter of triangle inscribed inellipse
I recently heard an interesting question via the grapevine:
Given an ellipse E in the plane, consider any point A of E. Then two other points B,C of E can be found so that the perimeter of the triangle ABC is maximized.
Denote this maximum perimeter by P(A).
Prove or disprove: P(A) is necessarily independent of A.
--Dan