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).

Obtuse Triangle -- from Wolfram MathWorld

Tucker Circles -- from Wolfram MathWorld

Kobon Triangles

Kobon Triangle -- from Wolfram MathWorld

Kobon Triangles: number of nonoverlapping ?s from $n$ lines - Online Technical Discussion Groups—Wolfram Community

Steiner Triangle -- from Wolfram MathWorld

Math Games: Kobon Triangles

MEDIAN Don Steward mathematics teaching: Kobon triangles

Obtuse Triangle -- from Wolfram MathWorld