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Another Fine Math You've Got Me Into...

Ian Stewart
Dover Publications
Publication Date: 
Number of Pages: 
[Reviewed by
Amy Shell-Gellasch
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He is that rare combination of one who knows and
loves mathematics on all its bewildering levels and
can write about them with zest and humor...

— Martin Gardner

Since I could not have spoken any more eloquently about Ian Stewart than Martin Gardner did in his foreword to Stewart's Another Fine Math You've Got Me Into... , I will let him continue. "To these skills he adds a fondness for recreational topics and amusing wordplay. It is impossible to read him without learning a great deal and thoroughly enjoying the instruction." I will add that Stewart is also a creative and playful storyteller, one you can not take your eyes off of for a minute, lest you miss something.

Ian Stewart is the fourth author of the immensely popular column Mathematical Recreations at Scientific American, first held by Martin Gardner under the title Mathematical Games. As each new recreational mathematics guru took up the post, the column changed focus and style to reflect the writer's personality and interests. The title of the column likewise changed to reflect this. Before taking up this illustrious position, Stewart wrote the column Visions Mathématiques for the French version of Scientific American. With Stewart now at the helm, Mathematical Recreations in many ways has returned to its original flavor. Yet the texture is all Stewart.

Like Gardner before him, Stewart has taken from both his Scientific American columns in creating this book. However, those columns are not just reproduced here. The themes and ideas from twelve columns have been melded together into sixteen chapters, each focusing on a particular mathematical topic, with myriad twists and turns. For example, the first chapter, The Lion, the Llama and the Lettuce, (which may be more familiar to you as the farmer with a boat, a fox, a sheep and a cabbage riddle) quickly passes through the territories of graph theory, determination of shortest paths, the Tower of Hanoi problem, and Sierpinski's triangle, all in fourteen pages. The amazing thing is that it all flows together logically and is a joy to read. However, you cannot just sit back and read it. Along the way Stewart challenges you to sit up and take notice of what he is doing. He does this by leaving just enough to the reader to spark your curiosity, as any good teacher or lecturer would do. He also poses specific "homework" problems along the way (with answers provided at the end.)

Other topics covered are: Tiling the plane coupled with combinatorics, logic and Venn diagrams, the calculation of area of lattice polygons, numbered paths on a pentagon, the Knight's tour on chess boards to tori, combinatorics and the projective plane, game theory, the couch around the corner problem... okay, enough of that. Put simply, Stewart covers topics ranging from graph theory to the geometry of the torus. Two chapters deal with topics further a field: evolution and music. Though both these chapters were mathematically interesting and piqued my curiosity, I felt rushed while reading them. The topics required more background and explanation than could be comfortably given in the space allotted. However, I think Stewart has two great book ideas waiting in these two topics.

Each of the sixteen chapters is presented with its own flair and style. Some are presented as a fairly straight-forward challenge to the reader. Most chapters are written in the form of a story about characters. Sometimes the lead character is Stewart himself, off on some vacation where his hosts invariably have some mathematically related problem that needs solving. In several chapters old Stewart favorites such as Henry Worm and his family appear. These chapters that intertwine mathematics with storytelling are my favorites. Stewart's flair for weaving a clever story with witty dialog around a mathematical idea is second to none. I believe this is what takes this book out of the realm of recreational mathematics and places it in a broader category, one of interest to a wide audience. Stewart uses pun and allusion to keep his readers on their toes in a literary and intellectual as well as mathematical and scientific sense. For example, the trials and tribulations of Quasimodulo kept me chuckling through the whole chapter on ringing a peal on a set of bells. (If you are unfamiliar with what a peal is in the world of bell ringing, it is just another example of the diversity of topics — nonmathematical — that Stewart introduces the reader to in the course of his mathematical journeys which makes this book such a joy.)

To conclude, even if you have a full recreational mathematics library, or any math library, or any library, this book should be added to it. It is a fun read for the mathematician, who will, I guarantee you, find a new way of looking at an "old" topic. It is a challenging yet enticing math teaser for amateur mathematicians. It is a wealth of ideas for the creative teacher of math or science at any level. Finally, it is an eye opening tour of the world of theoretical mathematics and its connections to the real world for any curious reader who enjoys being entertained while they learn something new.

Amy Shell-Gellasch is currently a freelance math historian living in Grafenwoehr Germany while her husband is on a three year tour of duty in Germany. She received her bachelor's degree from the University of Michigan in 1989, her master's degree from Oakland University in Rochester, Michigan in 1995, and her doctor of arts degree from the University of Illinois at Chicago in 2000. Her dissertation was a biographical piece on mathematician Mina Rees. Most recently, she conducted research with V. Fredrick Rickey on the history of the Department of Mathematical Sciences at the United States Military Academy, where she was an Assistant Professor.

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