  In general graph theory, the only relationship between vertices are expressed
via the edges. When the vertices are embedded in an Euclidean space, the
geometric relationships between vertices and edges can be interesting objects
of study. We look at the number of isosceles triangles where the vertices are
points on a regular grid and show that they satisfy a recurrence relation when
the grid is large enough. We also derive recurrence relations for the number of
acute, obtuse and right isosceles triangles.
