How Many Right Triangles Can You Find?

This Demonstration shows the number of right triangles that have their vertices at the points of an regular grid (so that the horizontal and vertical distance between points is the same). With "solution" checked, the number of triangles that have a right angle at the point , , is shown.

For example, for a 2x3 regular grid, the vertices of the 14 right triangles are:

{1,1},{1,2},{2,1}
{1,1},{1,3},{2,1}

{1,1},{1,2},{2,2}
{1,3},{1,2},{2,2}

{2,1},{1,2},{2,3}

{1,2},{1,3},{2,3}
{1,1},{1,3},{2,3}

{1,1},{2,1},{2,2}
{1,1},{2,1},{2,3}

{2,1},{2,2},{1,2}
{1,2},{2,2},{2,3}
{1,1},{2,2},{1,3}

{1,3},{2,3},{2,2}

{1,3},{2,3},{2,1}