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

intersection

γ(t)=(t²-1.t³-t)

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- July 31st 2010, 08:44 PMulysses123Self intersection
Show that the following curve is not closed and that it has exactly one self-

intersection

γ(t)=(t²-1.t³-t) - July 31st 2010, 10:36 PMTheEmptySet
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) - July 31st 2010, 11:36 PMulysses123
thanks thats nice and easy to understand, my teacher had confused me with his explanation.

- August 1st 2010, 04:15 AMHallsofIvy
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.