Abstract We classify the sets of four lattice points that all lie on a short arc of a circle that has its center at the origin; specifically on arcs of length tR 1/3 on a circle of radius R , for any given t > 0. In particular we prove that any arc of length on a circle of radius R , with , contains at most three lattice points, whereas we give an explicit infinite family of 4-tuples of lattice points, ( ν 1, n , ν 2, n , ν 3, n , ν 4, n ), each of which lies on an arc of length on a circle of radius R n .
