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corners theorem
In mathematics, the corners theorem is an important result, proved by Miklós Ajtai and Endre Szemerédi, of a statement in arithmetic combinatorics. It states that for every ''ε'' > 0 there exists ''N'' such that given at least ''εN2'' points in the ''N'' × ''N'' grid × , there exists a corner, i.e., three points in the form (''x'', ''y''), (''x'' + ''h'', ''y''), and (''x'', ''y'' + ''h''). Later, gave a simpler proof, based on the triangle removal lemma. The corners theorem implies Roth's theorem.
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