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Hello All,

I'm trying to prove something that we know that is correct but can't find how to do it or any example to show how to solve it.

Any 2-coloring of the scope of equilateral triangle must create a monochromatic rectangular triangle (That all of its vertexes and in the same color and they are positioned on the scope of the original triangle).

This problem is connected to Ramsey theory.

Does anyone know how to prove it ?



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I suggest you improve your question by adding some context. From where do you know that the statement is correct? And why are you interested in it? Right now the question looks too much like homework. – Sergei Ivanov Sep 11 '10 at 21:12
I assume a "rectangular triangle" is what I'd call a "right triangle," but I don't know what the "scope" of a triangle is. – Gerry Myerson Sep 12 '10 at 0:12
@Sergei Nice intuition. This is an old, classic contest problem. @Gerry The particular contest problem specified the boundary of an equilateral triangle. @itamar I noted that you posted another classic contest problem (the 30-60-90 right triangle variant) as an answer to a semi-related question a couple of days ago. While Ramsey theory is an interesting subject of genuine mathematical research, contest problems in their original form (without any interesting generalizations) are not appropriate here. That's what is for. – dvitek Sep 12 '10 at 1:14
Oh, I suppose I should have included a request to close. Thanks, magical people. – dvitek Sep 12 '10 at 1:14

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