Ray Beauregard (beau@math.uri.edu) received his B.A. from Providence College in 1964 and his Ph.D. in 1968 (under the guidance of Richard E. Johnson) from the University of New Hampshire. He has spent his entire career at the University of Rhode Island (Kingston, RI 02881). He and John Fraleigh are the co-authors of a textbook, Linear Algebra, currently in its third edition. Although most of his research has been in ring theory, he has recently become interested in elementary number theory. His… Expand

Summary The Alcuin number t(n) is equal to the number of incongruent integer triangles having perimeter n, where n is an integer. Using generating functions, we give a derivation of well-known… Expand

Ray Beauregard (beau@math.uri.edu) received his B.A. from Providence College in 1964 and his Ph.D. in 1968 (under the guidance of Richard E. Johnson) from the University of New Hampshire. He has… Expand

We present visual proofs of two lemmas that reduce the proofs of expressions for the lengths of the diagonals and the area of a cyclic quadrilateral in terms of the lengths of its sides to elementary… Expand