Experiencing Geometry, Physics, and Biology

The present book is the latest in a series of books by Professor Georg Glaeser and his coauthors highlighting geometric wonders for a general audience.  Many of the topics have been covered in more detail among numerous earlier books, but they are now attractively illustrated by around three hundred video links (via hyperlink and QR code).  More than a hundred topics are explored ranging over polyhedra, curves, surfaces, kinematics, astronomy, optics, fluid phenomena, and much more.  The preface notes that the present book was "created as a companion book for the freely available software Cross-Science" and this interactive dimension is a distinctive, enhancing the book’s effectiveness.

 

In my review of Prof. Glaeser's previous book Geometry and Its Applications, I likened that book to an expansive well-curated museum. By the same analogy, this book would be a select guided tour now aided by media technology and interactive exhibits.  The explanations in the present volume are sometimes terser, but the videos and accompanying software provide welcome pedagogic and interactive opportunities.  Among the over one hundred topics, some of my favorites were Cardan shafts, spherical trochoids, kaleidocycles, mobile mechanisms, ornaments on the Tassilo chalice, and moving ellipses on quadrics.  But there is sure to be something here to pique the curiosity of every reader.

 

The book is attractively produced and profusely illustrated.  I found little to quibble about: a small number of images reused from previous sources are in lower resolution or contain labels not in English; some simulations use unexplained parameters; in a few rare cases, the purport of a linked video was not entirely clear due to the terseness of the text.  But again, these are minor indeed.

 

As with the authors’ other works, the present book highlights how much we miss or take for granted by not being closely attentive to the world around us.  The strength of the book is in its inspiration and imagination rather than explanation (the details for which one can consult technical resources).  Even a reader dipping here and there will find much fodder for geometric intuition, imagination, and inquiry.  The book can serve as an auxiliary resource for a math appreciation course for general students, e.g. using its videos and the interactive software as trailheads for individual or group projects.  But I suspect the videos and interactive simulations may also appeal to younger readers, arousing them to wonder and inquiry though they may not yet know how to articulate a precise explanation.  And that is an admirable achievement.

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Jer-Chin Chuang is a Lecturer at the University of Illinois at Urbana-Champaign.