can someone help me with this proof- either give me advice on how to do it or get start or start me off and give a few pointers on what i should be doing..the proof is on the attachment. thanks

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- Jan 28th 2009, 11:55 AMdopiproof - curvature of plane curve
can someone help me with this proof- either give me advice on how to do it or get start or start me off and give a few pointers on what i should be doing..the proof is on the attachment. thanks

- Feb 6th 2009, 06:25 AMHallsofIvy
Well, what do you know about "curvature" and what formulas do you have for it? I suspect there are a number of different proofs of this starting from different formulas. You might, for example, use the fact that the curvature is $\displaystyle \left|\frac{dT}{ds}\right|$ where T is the unit tangent vector and s is the arclength. You would need to relate both parameters to the arclength. Then basically use the chain rule.