Kobon Triangle -- from Wolfram MathWorld

Kobon Fujimura asked for the largest number N(n) of nonoverlapping triangles that can be constructed using n lines (Gardner 1983, p. 170). A Kobon triangle is therefore defined as one of the triangles constructed in such a way. The first few terms are 1, 2, 5, 7, 11, 15, 21, (OEIS A006066). It appears to be very difficult to find an analytic expression for the nth term, although Saburo Tamura has proved an upper bound on N(n) of |_n(n-2)/3_|, where |_x_| is the floor function (Eppstein).

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Cleaver -- from Wolfram MathWorld

Stammler Triangle -- from Wolfram MathWorld

PDF) Congruent triangles in arrangements of lines

Parallelian -- from Wolfram MathWorld

List of unsolved problems in mathematics - Wikipedia

Triangle Counting -- from Wolfram MathWorld

Miquel Triangle -- from Wolfram MathWorld

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