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



