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CTK Exchange
Doug Ort
Member since Oct-7-07
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Oct-07-07, 12:28 PM (EST) |
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"Error in Cut The Knot Site"
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On https://www.cut-the-knot.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)(-1-3sqrt3, 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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