Imagine that a painter went down to a mathematical plane and colored all of the points on that plane one of three colors.
Prove that there exist two points on this plane, exactly one meter apart, that have the same color.
Consider an equilateral triangle, ABC, with side lengths √3/3 meters.
Add point C' which is the mirror image of C reflected across segment AB.
C and C' must be the same color, and they are one meter apart.
https://www.desmos.com/calculator/e45kx73mac
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Posted by Larry
on 2024-01-19 10:13:50 |
Slight variation with Desmos picture
