# Tagged Questions

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### What are interesting 3-colorings of the plane without rainbow lines?

This question is about 3-colorings of the plane in which every line is bichromatic (or monochromatic), i.e., there are no three collinear points of different colors. Such colorings trivially exist, ...
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### Minimizing the excursion of a sum of unit vectors

I have $n$ unit-length vectors $v_i$ in $\mathbb{R}^3$, whose sum is zero: $$v_1 + v_2 + \cdots + v_n = 0 \; .$$ Now I form the closed polygon $P$ in space by placing them head to tail. So the ...
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### On the number of lines of given points

Hi all, I have a question Concerning Beck's theorem. I have read it from http://en.wikipedia.org/wiki/Beck%27s_theorem and I have two questions : I suppose Beck's theorem doesn't hold when instead ...
Hello, What is a fast way to test whether a partial function can be extended to a chirotope of rank 3 ? That is: I have a domain $E = \{1,...,n\}$ and a partial function $f: E^3 \to \{-1, 0, 1\}$ ...