Geometric Design: An Artful Portfolio of Mathematical Graphics
by Christopher Alan Arthur
Self-published, Allen, TX, 2014
Reviewed by Phil Dyke
Back in the 1960s budding students of mathematics would look at and possibly buy books that told how to make elaborate models of polyhedra with names like the great stellated dodecahedron. These models were often then painted and decorated. This book by Arthur is a modern equivalent, but instead of cutting out cardboard, these days software (in this book Mathematica (c)) is used. Although hardly a replacement for Cundy and Rollett (1981), this is a delightful little book. It can simply be used as a picture book or for the more technical and ambitious, a self-study introduction for using mathematical software to produce art. However, budding mathematical artists will need access to Mathematica, which is expensive; there is cheaper mathematical software, but even student versions of these are not that cheap.
Without the old restrictions of cutting from cardboard, the scope of this little book is so much wider. The faces of complex solids can be bent and curved, surfaces can be changed in colour and drawn upon. Different delicate spidery constructions can be displayed and preserved on the screen; there are no breakages no clumsy mis-cuts, only programming errors that are corrected, how easily dependant on the expertise of the reader. The ability to try different styles and change the Mathematica code just a bit to get very different designs fits this modern era where sitting for hours with cardboard, scissors and glue is not as appealing to most. Then there are the self similar designs that go on forever--the Koch snowflake curve and, of course, the Mandelbrot gingerbread man, impossible to see before the computer graphic age, let alone build. This reviewer only has one qualm: Is the readership large enough? To construct these models from code, one needs considerable mathematical knowledge, and will the casual reader be satisfied with just looking? I notice from the frontispiece that the book is at present self-published. To the non-mathematician a large print coffee table edition of prints with no mathematics would probably be more appealing. To those who can digest the technicalities, it opens up a new world.
H.M.Cundy and A.R Rollett (1981) Mathematical Models. Tarquin Pub. 286 pp.