Question

Given a parametric equation r(t)=<(-t^2+4t-3), (3cos(pi*t)), (t^3-21t)> find where the curve intersects itself. This results in nasty non-linear systems of equations which I have no idea how to work with, help!

Answer 1

try solving this r(t) = r(t+k) both for t and k

Answer 2

http://www.wolframalpha.com/input/?i=solve+%28-t%5E2%2B4t-3%29%3D%28-%28t%2Bk%29%5E2%2B4%28t%2Bk%29-3%29%2C+%283cos%28pi*t%29%29+%3D+%283cos%28pi*%28t%2Bk%29%29%29%2C+%28t%5E3-21t%29%3D%28%28t%2Bk%29%5E3-21%28t%2Bk%29%29

Answer 3

im curious if the places it crosses itself are negative slopes

Answer 4

I use wolfram alpha to sole it before but I want to know how to do it