Akiyama’s book offers a heavily illustrated full color tour of Math Wonderland, an interactive museum of mathematics founded by the author in Japan in 2003. Although the apparent aim of the museum (and book) is to increase children’s interest in mathematics, adults, including professional mathematicians, will also find the work highly entertaining. I greatly enjoyed this work. There was a decent amount of material that was new to me, some of which I’ll make use of in undergraduate courses I teach.
The tour begins with the youths being given roller skates with wheels that are not round. Somehow they roll smoothly anyway! The children then learn about curves of constant width and see other examples and counterexamples. Later they are given sandbags to equalize their weights and sent simultaneously down different sliding boards. One board always provides the quickest descent and they then learn about the brachistochrone.
Other topics include the Pythagorean theorem, conic sections (with applications), tilings (how to easily create Escher-like designs), and various manipulations of Möbius strips. If one joins two Möbius strips with different twists perpendicular to one another and cuts each in half, the result is linked hearts — this was new to me and could make a cute Valentine’s day gift when done on red or pink paper. It simply looks like paper handcuffs to the recipient until he or she does the cutting!
There are 47 references provided at the end, of which 17 are websites. The remainder range from popularizations to research papers, including some by Yakiama himself. MAA members may have seen his paper “Tile-Makers and Semi-Tile-Makers” in the August-September 2007 issue of The American Mathematical Monthly. The man ideas of this paper are presented in the present book at a level that children can understand.
The only criticism I can offer is that no indication is given of the proper pronunciation of words that children will likely find difficult. Examples include Rouleaux, epitrochoid, brachistochrone, tautochrone, eejanaika, Baumkuchen, and extracorporeal shockwave lithotripsy. However, with these exceptions, the text should not present difficulties to a young reader (or a non-mathematician parent).
I strongly recommend this work to anyone who teaches mathematics from the level of elementary school up through undergraduate.
A link for downloading the first chapter is available at the publisher's web site.
Craig Bauer is the editor-in-chief of Cryptologia, a quarterly journal devoted to all aspects of cryptology (mathematical, historical, & pedagogical).