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Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.

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1975_01_01_erdos_graham_montgomery_rothschild_spencer_straus: Theorem 1 of the 1975 colloquium paper reduces a triangle to its three equilateral side lengths, and its ladder, roulette and five-point methods prove several triangle families Ramsey in the two-colored plane; claimed.

1976_05_01_shader: Shader's 1976 theorem that every two-coloring of the plane contains a monochromatic congruent copy of every right triangle, with two further one-parameter families of triangles; refereed, in J. Combin. Theory Ser. A.

2024_02_22_currier_moore_yip: Every two-coloring of the plane contains a monochromatic congruent copy of three equally spaced collinear points, hence of every (a, 2a, xa) triangle with x in [1,3]; refereed, in Combinatorica 44 (2024).