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A Ludic Journey into Geometric Topology

Ton Marar
Publication Date: 
Number of Pages: 
[Reviewed by
Timothy Clark
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The preface to A Ludic Journey into Geometric Topology quickly draws the reader in with colorful images of Pac-Man, describing the toroidal landscape in which his digital adventures take place. This immediately sets the tone of the book and serves to motivate the primary themes within, namely geometry, topology, and humanity's efforts to understand our place in the universe. As the title suggests, the author attempts to engage the reader in a playful discussion on these ideas.
The back cover does a good job describing the contents and organization of the book.
The text begins with a discussion of mathematical models, moving on to Platonic and Keplerian theories that explain the Cosmos. Geometry from Felix Klein's point of view is then presented, paving the way to an introduction to topology. The final chapters present the concepts of closed, orientable, and non-orientable surfaces, as well as hypersurface models.
Generally, the exposition swiftly guides the reader along with motivating examples, philosophical questions, intuition, historical development, and modern context. Along the way, inspiration is taken from art, architecture, astrophysics, literature, religion, and more. Overall, this is a particularly well-named book—the conversational exposition, plethora of colorful diagrams, and interesting collection of topics do indeed produce a ludic intellectiual journey suitable for experts and non-experts alike. 
Each section ends with a list of suggested reading, but there are no exercises.  Very little prior mathematical knowledge is assumed – some topics are more difficult than others, but generally speaking, the text should be approachable to anyone who is at least moderately interested in mathematics.  While some level of mathematical rigor is maintained, I expect this would not work well as a traditional mathematics textbook.  That said, I think it would make a great source of entertaining supplemental reading for an undergraduate course related to geometry or topology.
Timothy Clark is an Associate Professor at Adrian College. His area of research is algebraic topology.