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).

Math Games: Kobon Triangles

Kobon Triangle -- from Wolfram MathWorld

Parallelian -- from Wolfram MathWorld

Math Games: Kobon Triangles

Lune -- from Wolfram MathWorld, lune

PDF) Congruent triangles in arrangements of lines

Tucker Circles -- from Wolfram MathWorld

Steiner Triangle -- from Wolfram MathWorld

Parallelian -- from Wolfram MathWorld

Triangle Counting -- from Wolfram MathWorld