Thread: Self intersection

Show that the following curve is not closed and that it has exactly one self-
intersection

γ(t)=(t²-1.t³-t)

Let be the times where the curve intersects with then
and and
and

Subtracting the x equations gives

Since

Plugging into the y equations and subtracting gives

So the curve intersects itself when t=-1 and t=1 at the point (0,0)

thanks thats nice and easy to understand, my teacher had confused me with his explanation.

Also, note that as t goes to infinity, both and go to infinity but as t goes to negative infinity, [tex]t^2- 1[tex] goes to infinity while goes to negative infinity. That shows that the path is not closed.