Re: simple question....very simple

*To*: mathgroup at smc.vnet.net*Subject*: [mg23717] Re: simple question....very simple*From*: Hartmut Wolf <hwolf at debis.com>*Date*: Mon, 5 Jun 2000 01:09:12 -0400 (EDT)*Organization*: debis Systemhaus*References*: <ZrWY4.9633$aa7.59764@nlnews00.chello.com>*Sender*: owner-wri-mathgroup at wolfram.com

B schrieb: > > I'm looking for the funktion to describe a oval.... > Hello Ben, the question of course is, what do you consider as an oval, and how do you want to hold it in your hands: parametric, implicit, ... I assume here oval as "being shaped like an egg" and such won't offer neither an ellipse nor a race track (Indycar or whatever). To stay succinct let's use a helper ... poly[coefficients_, var_] := coefficients.var^Range[0, Length[coefficients] - 1] ... to make a polynom. So look at With[{n = 6, p = 2}, ParametricPlot[ Evaluate[{poly[Prepend[1/Range[n]^p, 0], Cos[2 Pi t]], Sin[2 Pi t]/Sqrt[2]}], {t, 0, 1}]] To me this seems to be pretty egg-shaped. (You may like to experiment with n, certainly with n -> Infinity the tip may get too pointed). Whereas With[{n = 3, p = 1}, ParametricPlot[ Evaluate[{poly[Prepend[1/Range[n]^p, 0], Cos[2 Pi t]], Sin[2 Pi t]/Sqrt[2]}], {t, 0, 1}, PlotRange -> All]] might be considered less well-shaped, although you might have been served that soft-boiled quite often. A way to get "the ideal egg" might be to look at the process of egg formation *), derive an ODE for that and solve. For the moment, I lack the imagination to do that. What about you MathGroup? [So taking the 3rd power (p = 3), and n -> Infinity (egg doesn't vary much with n) looks marvellous, but why?] -- Hartmut Wolf --------- *) consulting the experts with eggs -- the birds -- you will see there are different solutions, e.g. there are special, cone-shaped eggs as not to roll off the cliff and get lost in the sea.