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Teaching Mathematics and its Applications Advance Access originally published online on June 26, 2007
Teaching Mathematics and its Applications 2007 26(4):187-195; doi:10.1093/teamat/hrm012
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© The Author 2007. 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

Does a cube have an equation?

Pavel Satianov and Michael N. Fried

Addresses for correspondence: Pavel Satianov, Sami Shamoon College of Engineering, Beer Sheva, Israel. E-mail: pavel{at}sce.ac.il Michael N. Fried, Program for Science and Technology Education, Ben Gurion University of the Negev, Beer Sheva, Israel. E-mail: mfried{at}bgu.ac.il

Submitted December 2006; accepted May 2007

This article looks at the question of whether and how a geometrical cube may be determined as the solution set of a single equation. Beyond this being an interesting and surprising result for upper high school and first year college students, we argue that, as an investigative activity, it has value in refining students’ images of what solutions of equations can be and, with that, refining their ideas of what an equation is.

Pavel Satianov is a senior lecturer in mathematics at the Sami Shamoon College of Engineering. He received his MS from the mathematics department of Novosibirsk State University in 1970 and his PhD from the mathematics department of St Petersburg State Pedagogical University in 1984 with a thesis on the Use of Problems with Graphs in Teaching Calculus (advisor Prof. A. Myshkis). His interests include tertiary education, pedagogical strategies for developing creative mathematical thinking, graphical approaches for teaching analysis and the application of graphing calculators in mathematics education. He has written more than 50 articles and books.

Michael N. Fried is a lecturer in the Program for Science and Technology Education at Ben Gurion University of the Negev. His undergraduate degree in the liberal arts is from St John's College in Annapolis MD (the ‘great books’ school). He received his M.Sc. in applied mathematics from SUNY at Stony Brook and his PhD in the history of mathematics from the Cohn Institute at Tel Aviv University. His research interests are eclectic and include mathematics pedagogy, mathematics teacher education, sociocultural issues, semiotics, history of mathematics and history and philosophy of education. Besides his papers in mathematics education, he is author of two books: (with Sabetai Unguru) Apollonius of Perga's Conica: Text, Context, Subtext (Brill, 2001); Apollonius of Perga, Conics IV: Translation, Introduction, and Diagrams (Green Lion Press, 2002).


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