By A Mystery Man Writer
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).
Kobon Triangles: number of nonoverlapping ?s from $n$ lines - Online Technical Discussion Groups—Wolfram Community
Central Triangle -- from Wolfram MathWorld
Fuhrmann Triangle -- from Wolfram MathWorld
MEDIAN Don Steward mathematics teaching: Kobon triangles
UnitTriangle—Wolfram Language Documentation
Lune -- from Wolfram MathWorld, lune
Steiner Triangle -- from Wolfram MathWorld
Math Games: Kobon Triangles
Gergonne Line -- from Wolfram MathWorld
Fuhrmann Triangle -- from Wolfram MathWorld