Date: Mar 3, 2013 10:16 PM
Author: Brad Cooper
Subject: Curvature on a curve and circle
The "well behaved, smooth" function f(x) has endpoints f(0) = f(h) = 0. The

curve of the function has length s1.

An arc of a circle passing through (0, 0) and (0, h) has fixed curvature k

and its arc length is also s1.

It is required to show that a point must exist on f(x) where curvature is

also k.

I have set up a CAS program to simulate the situation and the proposition

held up in every case.

I have been working with the idea that, at the required point, the normal to

f(x) is normal to the circle.

I am not making much headway. Any ideas appreciated.

Cheers,

Brad

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