In this 2-by-3 grid, each lattice point is one unit from its nearest neighbors. A total of 14 isosceles triangles (but not right triangles), each with an area of 1/2u^{2} have only two vertices that are one unit apart in the grid. How many such half-unit triangles have at least two vertices in an x-by-y grid?

Guest Oct 19, 2019