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Unread 14-12-2012, 23:23
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DampRobot DampRobot is offline
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AKA: Roger Romani
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Re: numerical computation contest

Ether,

I'm not a programmer, but I love a good geometrical challenge.

The equations I came up with were: (r-h)sin(l/2r)=x/2 and 2rsin(l/2r)=(x^2/4+h^2)^1/2
where r was the radius of the curve, h was the height specified in your diagram, l was the length of the curve, and x was the length of the chord. To find the numerical solution, input values for l and x, and solve for h or r.

Was the "challenge" to write a program that found the solutions of these functions through guess and check? Or did I come up with a different solution? Plugging in the values on this thread with my trusty graphing calculator, I got a reasonable approximation of the answers posted on this thread.
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