This volume had its origin in a Contributed Papers Session on “Using History of Mathematics in your Mathematics Courses” at the Joint Mathematics Meetings in 2006. Rather than simply being a set of articles about the history of mathematics, the work attempts to be immediately useful to the classroom teacher. To a large extent, it succeeds in its goal.
The individual chapters (the editors call them Time Capsules) in the volume are very mixed in style, content, mathematics level, and length. Although this has some benefits (there is something here for everyone), it also has some drawbacks (a lack of uniform style makes using the text more difficult). I will first comment on some of the problems with the book before describing its (many!) great qualities.
The variations in the chapters go deeper than just the writing style. Some of the chapters include a section of problems and questions for students. Others do not. Still others include questions, but only in an appendix in an unlabeled section. The chapters are laid out in a uniform and very useful way, with consistent sections: Introduction, Historical Background, In the Classroom, and Conclusion — except sometimes they aren’t. Of the 35 chapters, about ten do not follow this format (including, puzzlingly, four authored by one of the book’s editors). In practice this means that while many of the chapters can be easily adapted for classroom use, some cannot.
These quibbles, however, ought not distract us from the large amount of good work and excellent content contained therein. Many of the chapters are quite wonderful. I mention a few of these to give an overall flavor of the book:
- Lawrence D’Antonio’s How to Measure the Earth gives several methods one could use to determine the size of the Earth, using mountains, stars, or shadows. For each of these the author gives a good mathematical explanation, but also documents when historically the method was used. All of these are followed by many good suggestions for problems and projects for students. The material is fascinating, useful, and is here collected in a way I’ve never seen before.
- Victor Katz’s Copernican Trigonometry leads the reader through the calculation of a trigonometric table in a historically accurate way. In the process, students learn or review almost every formula learned in a trigonometry class. The chapter is laid out in such a way that one could lecture from it directly, or even pass out (with permission!) copies to students.
- Daniel Curtin’s Descartes’ Approach to Tangents is short reminder that mathematicians calculated tangent lines before the development of calculus. It could be quickly and easily used to put together a good lecture, and the provided questions would make for a good small take-home project.
- Clemency Montelle’s A ‘Symbolic’ History of the Derivative may be my favorite chapter in the book. It concisely and convincingly demonstrates the importance of notation in the history of mathematics. This topic is not discussed often enough in math or math history classes, and this chapter makes for a great introduction to the subject.
- Daniel Otero’s Plimpton 322: The Pythagorean Theorem, More than a Thousand Years before Pythagoras is a self-contained introduction to Plimpton 322, and more generally to Babylonian mathematics. It is designed to be used over two class sessions, and contains specific recommendations to instructors as to how to run each day of class.
As can be seen from this small sample, there are a wide range of topics covered, and a wide variety of styles in which chapters are written. Together they compose a valuable offering to the classroom teacher. I have recommended this book to high school teachers with an interest in incorporating history in the classroom, secure in the knowledge that they can pick up the book and start to use it immediately.
In summary, this is an interesting and useful book, which lives up to its stated goals.
Dominic Klyve is an assistant professor of mathematics and statistics at Central Washington University. He enjoys mathematics, history, and time capsules.