Suppose the 2-d plane is coloured in two colours. You are given a right angled triangle of given dimensions. Prove that there exists a monochromatic copy(i.e the vertices are of same colour) of the given triangle on the plane.
Existence of a Right angled triangle in a two coloured plane
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$\begingroup$
triangles
combinatorial-geometry
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0Your plane is restricted to points with **integer coordinates**, isn't it ? – 2017-01-24
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0It's R^2 probably. – 2017-01-24
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0Tough to do with integer coordinates if your right-angled triangle has a side of non-surd length. – 2017-01-24
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0No the plane is not restricted to integer coordinates. – 2017-01-25
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0Connected [same problem with 3 colors](http://math.stackexchange.com/q/1508249) – 2017-01-26
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0One thing again: you should say that it is only the vertices of the triangle that should be with a same color (monochromatic). – 2017-01-26