Post #3179045

@isaackuo@spacey.space Sure. In more detail, the full configuration space for this problem is the set of all pairs of points in the interior of the triangle T, which is a 4-dimensional set, T x T, which can be split into 3 subsets consisting of pairs of points such that the line through them intersects the 3 different pairs of sides of the triangle. Any linear transformation that acts on the plane to map T into an equilateral triangle E also acts on R^4 to map T x T into E x E, while preserving all the ratios between the 4-volumes of the subsets of T x T associated with the 3 different outcomes.