MATRIX MAGIC AND RECURSIVE RIDDLES

Abstract

The Euclidean algorithm finds the greatest common divisor of a pair of positive integers recursively by forming a new pair consisting of the smaller number and the remainder of the larger divided by the smaller. Formulating this procedure using matrices and using their associativity and determinant properties gives results about continued fractions. This expository paper explores related matrix methods to locate polynomial roots, propagate waves, and design filters, fractals, and wavelets.