Here's an idea, inspired by Frank's message. (Apologies if this is equivalent to what someone has posted previously.) Let's modify the equation of an ellipse (x/a)^2 + ((y + k)/b)^2 = 1 by making k, instead of a constant, a function of y. One simple choice is k = c(b^2 - y^2), where c is a constant. Then a and b determine width and length, and their ratio determines eggcentricity, while c determines the index of ovalitude. A nice chicken-egg shape is obtained using a = 3, b = 4 and c = 0.03 . David W. Cantrell ----- Original Message ----- From: <franktaw@netscape.net> To: <math-fun@mailman.xmission.com> Sent: Tuesday, February 27, 2007 20:55 Subject: Re: [math-fun] Re: Simplest Ovals
Actually, I would think that two degrees of freedom is the ideal: one for how long the oval is compared to its width (eccentricity), and one for relative size of big end vs. small end (ovalicity?).
Franklin T. Adams-Watters