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Topic: Curvature on a curve and circle
Replies: 6   Last Post: Mar 11, 2013 3:54 PM

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 Brad Cooper Posts: 169 Registered: 12/8/04
Curvature on a curve and circle
Posted: Mar 3, 2013 10:16 PM

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,

--
Number of stars = 10 x Number of grains of sand on all the beaches and
deserts of Earth.

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