Differential Geomtery. Find the vertices the equation

[ocho]

Find the vertices of α(t) = 1 - 2 cos(t)

I know that to find the vertices we have to set the curvature equal to zero.

Curvature = ||α'(t) x α''(t)|| / (||α'(t)||^3)

I know the first and second derivative of α. But I feel like I am missing something. Should I do a step before taking the derivatives.

Thanks

 

[chiro]

Hey ocho and welcome to the forums.

If you can do the problem correctly in one go, then just do it and if you're concerned check it afterwards (possibly with another attempt that breaks things up a bit).

Math is math and if you know what's going on and what's happening then the answer is the answer and one that is based on understanding and proper technique.

Maths is fortunate (like anything really) in that you can obtain the answer in many different ways since there is no one method that is prioritized to give an answer that no other method will not, so if you choose a way to solve something based on sound principles and technique, then that's what really matters.

 

[lavinia]

Find the vertices of α(t) = 1 - 2 cos(t)

I know that to find the vertices we have to set the curvature equal to zero.

Curvature = ||α'(t) x α''(t)|| / (||α'(t)||^3)

I know the first and second derivative of α. But I feel like I am missing something. Should I do a step before taking the derivatives.

Thanks

I don't see what the curve is. Is it in the plane or in 3 space? What you wrote down just seems to be a function.