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Fermat Toricelli Geometric Proof

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Phil Todd

@polymnia

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We use rotations to construct a path equal in length to the sum of the distances AE+BE+CE, whose end points are fixed.  Minimum for AE+BE+CE occurs when this path is a straight line.

So long as no angles of the original triangle are greater than 120 degrees, this works.  What goes wrong when an angle does exceed 120 degrees?

Tags: mechanics, fermat
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