In finding the average area 
of a triangle chosen from a closed, bounded, convex region
of the plane, then 
, for 
any nonsingular affine transformation of the plane.
Point Picking
See also
18-Point Problem, Ball Line Picking, Ball Triangle Picking, Cube Line Picking, Cube Point Picking, Cube Tetrahedron Picking, Cube Triangle Picking, Discrepancy Theorem, Disk Line Picking, Disk Point Picking, Disk Triangle Picking, Happy End Problem, Line Line Picking, Line Segment Picking, Line Point Picking, Planar Distance, Simplex Simplex Picking, Sphere Line Picking, Sphere Point Picking, Sphere Tetrahedron Picking, Sylvester's Four-Point Problem, Tetrahedron Picking, Triangle Picking, Triangle Point PickingExplore with Wolfram|Alpha
References
Pfiefer, R. E. "The Historical Development of J. J. Sylvester's Four Point Problem." Math. Mag. 62, 309-317, 1989.Referenced on Wolfram|Alpha
Point PickingCite this as:
Weisstein, Eric W. "Point Picking." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PointPicking.html