Square triangle picking is the selection of triples of points (corresponding to endpoints of a triangle) randomly placed inside a square. n random triangles can be picked in a unit square in the Wolfram Language using the function RandomPoint[Rectangle[], {n, 3}]. Given three points chosen at random inside a unit square, the average area of the triangle determined by these points is given analytically by the multiple integrals A^_ | = | ( integral_0^1 integral_0^1 integral_0^1 integral_0^1 integral_0^1 integral_0^1 left bracketing bar Δ right bracketing bar d x_1 d x_2 d x_3 d y_1 d y_2 d y_3)/( integral_0^1 integral_0^1 integral_0^1 integral_0^1 integral_0^1 integral_0^1 d x_1 d x_2 d x_3 d y_1 d y_2 d y_3) | = | integral_0^1 integral_0^1 integral_0^1 integral_0^1 integral_0^1 integral_0^1 left bracketing bar Δ right bracketing bar d x_1 d x_2 d x_3 d y_1 d y_2 d y_3.

cube tetrahedron picking | Heilbronn triangle problem | hexagon triangle picking | obtuse triangle | polygon triangle picking | square line picking | Sylvester's four-point problem | triangle triangle picking | unit square