If every point in the plane R^2 is colored red or blue.Prove that given a^2+b^2=c^2 a,b,c are real numbers, one can find a monochromatic triangle with the sides a,b,c respectively. (Also is the answer true for more than 2 colors. Provide a proof or counter example adequately.)
Finding a monochromatic right angled triangle of any side.
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combinatorial-geometry
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0I assume the plane is $\mathbb{Z}^2$, not $\mathbb{R}^2$... – 2017-01-24
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0Please provide your attempts. – 2017-01-24