Electronic Proceedings of the Eleventh Annual Conference on Technology in Collegiate Mathematics


Product of Shears

Gina M. Foletta
Northern Kentucky University
Department of Mathematics
Highland Heights, KY 41099-1700
Phone: (606) 572-6349
E-mail: foletta@nku.edu


In our college geometry course, shears are a small component of our treatment of transformational geometry. Yet, shears are important because they counteract the commonly held belief that all transformations are isometries - or at least similitudes. While I was consulting for the CAS-Intensive Mathematics Project (A curriculum development project [NSF-ESI-9618029] directed jointly from The Pennsylvania State University and The University of Iowa.) this summer, a colleague posed a question: "Are you aware that rotations are implemented on some dynamic geometry tools as a product of three shears?" After my initial response of skepticism, I began to explore the question.

My investigation resulted in the following theorem: A rotation about the origin is the product of three shears. In the proof I used shears about the x-axis and y-axis. The paper elaborates on this theorem and discusses several teaching issues.