All triangles are equilateral

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

stand 1:28 AM on 3 Jan 2007

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.

Ed Davies 6:31 PM on 5 Jan 2007

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.

Bolt 3:00 AM on 2 Apr 2014

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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