Electronic Proceedings of the Eleventh Annual International Conference on Technology in Collegiate MathematicsNew Orleans, Louisiana, November 1922, 1998Paper C044
Product of Shears 
Gina M. Foletta
Department of Mathematics
Northern Kentucky University
Highland Heights, KY 410991700
USA
Phone: (606) 5726349
foletta@nku.edu

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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 CASIntensive Mathematics Project (A curriculum
development project [NSFESI9618029] 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 xaxis and
yaxis. The paper elaborates on this theorem and discusses several teaching issues.
Keyword(s): geometry