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