MathGroup Archive 2002

[Date Index] [Thread Index] [Author Index]

Search the Archive

Parametric curve cutting itself

  • To: mathgroup at smc.vnet.net
  • Subject: [mg34187] Parametric curve cutting itself
  • From: "Per Lundgren" <yesgoyes at ebox.tninet.se>
  • Date: Wed, 8 May 2002 01:58:00 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Looking at the ParametricPlot[{(Cos[6 t])^2, 2Sin[7 t]}, {t, 0, 3Pi/7}] 
shows it cuts itself at four pairs of values of  t. How do I find these 
four points with an accuracy of 1x10^-7 ?

I know this problem can be solved exactly looking at the conditions 
where:

Cos[6s] == +Cos[6t] or -Cos[6t]
Sin[7s]==Sin[7t]

but I am also looking for the approximative way using the accuracy 
condition above and some kind of iterating function (I think) makes the 
job. Is there some built-in function in Mathematica solving this kind of 
"parametric curve cutting itself"-problems.

Thank you in advance
Per Lundgren, Sweden


  • Prev by Date: Physical memory leak in Mathematica ?!
  • Next by Date: double integral
  • Previous by thread: Re: Physical memory leak in Mathematica ?!
  • Next by thread: double integral