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Doug Ort
Member since Oct707

Oct0707, 12:28 PM (EST) 

"Error in Cut The Knot Site"

On https://www.cuttheknot.org/Generalization/fermat_point.shtml, in the second line of the discussion after Solution 1 there is the following statement: (A variant of Napoleon's theorem claims that triangle A'B'C' is also equilateral.) This claim is bogus. The triangle with vertices A=(0,3), B=(1,0), C=(1.0) has A'=(0,sqrt3), B'=(1/2)(1+3sqrt3,4) and C'=(1/2)(13sqrt3, 4), and a simple calculation shows that the distance between A' and B' is not equal to that between B' and C'. 

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