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Teaching Mathematics and its Applications Advance Access originally published online on November 28, 2008
Teaching Mathematics and its Applications 2009 28(1):48-52; doi:10.1093/teamat/hrn019
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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

The wonky trammel of Archimedes

Chris Sangwin{dagger}

School of Mathematics, University of Birmingham, Birmingham, B15 2TT, UK

{dagger}Email: C.J.Sangwin{at}bham.ac.uk

Submitted July 2008; accepted September 2008

This article examines the ellipsograph of Archimedes, also known as the locus problem of Franciscus van Schooten, and related mechanisms. We not only solve the algebraic system explicitly, but we also reverse engineer the problem and find configurations that provide a particular solution. Using the modern techniques of polynomial Gröbner Bases we show this can be used as a traditional compass, as a straight edge (to draw a straight line) and as an ellipsograph to trace ellipses.

Chris Sangwin is a lecturer in the School of Mathematics at the University of Birmingham, UK and Research Fellow for the Maths Stats and OR Network, part of the Higher Education Academy. His educational research focuses on using computer algebra systems for assessment of mathematics.


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