Remarkable Floor Function Identity With Geometrical Interpretation, Lattice Point Connection

floor(a/b) + floor(2a/b) +...+ floor((b-a)a/b)) = (b-1)(a-1)/2, Super cool geometric interpretation of a floor function Identity(related to interior lattice points) that I found in Loren C. Larson’s problem solving book. Just Floorrific! Huh Doctor Penn. Nice working definition of the fractional part function is the value of the real number minus the floor of the real number. @DrBarker was intrigued by this floor identity and verified it by purely algebraic analytic means without appealing to its formulation from a rectangular grid of lattice points.