In a recent article (this Gazette, 65 (1981), 87-92) Dr Anderson raised the question of the derivation of the well-known formula for the sum of integer squares, in contradistinction to its mere verification by induction. Some time ago, in response to a request from a colleague, I derived each of the well-known formulas

by arguments based upon the decomposition of rectangles. As a complement to Dr Anderson’s article, these may be of interest; especially, in view of the derivation, to those requiring the formulas for elementary integration from first principles.