The wonky trammel of Archimedes

Author: Sangwin, Chris

Source: Teaching Mathematics and its Applications, Volume 28, Number 1, 27 March 2009 , pp. 48-52(5)

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Abstract:

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.

Document Type: Research article

DOI: http://dx.doi.org/10.1093/teamat/hrn019

Publication date: 2009-03-27

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The journal provides a forum for the exchange of ideas and experiences which contribute to the improvement of mathematics teaching and learning for students from upper secondary/high school level through to university first degree level. A distinctive feature of the journal is its emphasis on the applications of mathematics and mathematical modelling within the context of mathematics education world-wide. The journal's readership consists of mathematics teachers, students, researchers and those concerned with curriculum development and assessment, indeed anyone concerned about the education of users of mathematics.