Euler's formula for the polyhedron, V – E + F = 2, is simply fascinating. But when we hold in our hands a physical model of a dodecahedron, it seems that the formula comes triumphantly to life. Very similar feelings of fascination occur when playing with, say, Rubik's cube or other geometric games and models of mathematical objects. Our most enhanced sense of perception is the vision, so it is only natural that we enjoy admiring complex geometrical models with our own eyes, in the same way that we fully enjoy music with our hearing. The teacher should exploit this fascination in the classroom (especially in elementary and middle school) by complementing the lecture with hands-on activities where the students actually touch, see and hear mathematics.
Hands On History is a compilation of 16 articles that combine our fascination for mathematical devices and models with the rich history of mathematics. Each article explains how to build one of these devices (either by the instructor or the students themselves), the history behind it, and how to incorporate the model in a classroom setting.
The topics are the following: construction of labyrinths, multiplication with Napier's bones, the towers of Hanoi, rectangular protractors, Pythagoras theorem, geometric string models of ruled surfaces, French curves and other historical mechanisms to drawing curves, making your own planimeter, learning from Roman land surveyors (a mathematics field exercise), geometry in Greek astronomy, construction and history of Sundials, squares and cubes, the cycloid pendulum clock of Huygens, building a brachistochrone and a guide to exhibiting mathematical objects.
As you can see, the topics are very varied. Some of the devices seem to be only of nostalgic value, and perhaps only of interest to mathematicians and historians, but not so much to a student. However, many of the topics seem to have a great potential for a fun and interesting classroom activity. Some of them may be quite challenging to construct, but many should be straightforward. The book contains many illustrations, photographs and blueprints to help in the construction of these devices. I believe the book has achieved its own goal: it is a great resource for the teacher who wants to add some hands on (historical) activities in the classroom.
Álvaro Lozano-Robledo is H. C. Wang Assistant Professor at Cornell University.