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Teaching Mathematics and its Applications Advance Access originally published online on October 8, 2008
Teaching Mathematics and its Applications 2008 27(4):174-186; doi:10.1093/teamat/hrn017
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© The Author 2008. Published by Oxford University Press on behalf of The Institute of Mathematics and its Applications. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

Rolling Squares

Derek Holton and Carol Knights

Address for correspondence: Prof D Holton, Department of Mathematics and Statistics, University of Otago, Box 56, Dunedin, New Zealand. Tel: 064 3 479 7758, Fax: 064 3 8427, E-mail: dholton{at}maths.otago.ac.nz

Submitted April 2008; accepted August 2008

Here, we investigate what loci are produced when a square of side-length one is allowed to rotate around a square of side-length n, where n is a whole number. We find that if i = 1, 2, 3 or 4 (mod 4), the loci obtained for n {equiv} i (mod 4) all have the same symmetry and we show how the perimeter of each class can be determined. We also analyse the case of rotation of a square of side-length one about a rectangle of dimensions m x n when m and n are whole numbers. A similar result is obtained for classes of rectangles modulo 4 to that obtained in the square case. Finally, we suggest that this is a useful investigation to undertake with secondary school pupils. We discuss how we have used this investigation with such a group.

Derek Holton is currently Professor of Pure Mathematics at the University of Otago; researches in the areas of Graph Theory and Mathematics Education (mainly areas relating to problem solving); enjoys working with students of all ages.

Carol Knights is currently a principal lecturer in mathematics education at the University of Chichester. Previously, she taught across the 11–18 age range in Hampshire for 14 years as Head of Department and Advanced Skills Teacher working with a range of schools to improve attainment and engagement in mathematics. She has wide expertise in the use of ICT in the classroom and has authored resources for both the Bowland key stage 3 mathematics initiative and the GE STEM Achievement in Mathematics London Pilot. She currently leads the Chichester team in coordinating the work of the NCETM in the South East Region.


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