Tuesday 2 January 2007
Here is a “proof” that all triangles are equilateral. Can you see what is wrong?
Wikipedia lists lots more of these false proofs, including the answer to the puzzle of what’s wrong with the equilateral proof.
Tuesday 2 January 2007
Here is a “proof” that all triangles are equilateral. Can you see what is wrong?
Wikipedia lists lots more of these false proofs, including the answer to the puzzle of what’s wrong with the equilateral proof.
Comments
Well, I don't know if this is the reason, but it seems that it is possible to construct a triangle where the point M lies outside the triangle.
Can you see what's wrong? Yes, I think so. Should I post it or would that ruin the fun for anybody? I'll just say that I think stand's comment above is in the right direction but not strong enough.
In case AB is not equal to AC, M lies outside the triangle. If that's the case, |AC|=|RC|-|AR|, and not |AC|=|RC|+|AR|, as stated in the proof.
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