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MathGroup Archive 2000

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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.



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