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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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Fuhrmann Triangle -- from Wolfram MathWorld
Fuhrmann Triangle -- from Wolfram MathWorld
Kobon triangles
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Obtuse Triangle -- from Wolfram MathWorld
Kobon Triangle -- from Wolfram MathWorld
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Fuhrmann Triangle -- from Wolfram MathWorld
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PDF) Congruent triangles in arrangements of lines