What is the formula for curvature in a plane curve?

themadhatter1
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Homework Statement


show that the curvature of a plane curve is \kappa=|\frac{d\phi}{ds}| where phi is the angle between T and i; that is, phi is the inclination of the tangent line.

Homework Equations


The Attempt at a Solution



I'm not sure how to start this one out.

Any ideas?
 
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Well, what is your definition of curvature? (Some texts use the formula you give as the definition of curvature. Obviously your text does not but we need to know what definition it does use to say where you should start.)
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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