Visualizing Mathematics with 3D Printing

With the book in one hand and a 3D printed model in the other, readers can find deeper meaning while holding a hyperbolic honeycomb, touching the twists of a torus knot, or caressing the curves of a Klein quartic.

Wouldn't it be great to experience three-dimensional ideas in three dimensions? In this book-the first of its kind-mathematician and mathematical artist Henry Segerman takes readers on a fascinating tour of two-, three-, and four-dimensional mathematics, exploring Euclidean and non-Euclidean geometries, symmetry, knots, tilings, and soap films. Visualizing Mathematics with 3D Printing includes more than 100 color photographs of 3D printed models. Readers can take the book's insights to a new level by visiting its sister website, 3dprintmath.com, which features virtual three-dimensional versions of the models for readers to explore. These models can also be ordered online or downloaded to print on a 3D printer. Combining the strengths of book and website, this volume pulls higher geometry and topology out of the realm of the abstract and puts it into the hands of anyone fascinated by mathematical relationships of shape. With the book in one hand and a 3D printed model in the other, readers can find deeper meaning while holding a hyperbolic honeycomb, touching the twists of a torus knot, or caressing the curves of a Klein quartic.

When someone unfamiliar with mathematics walks into my office expecting an explanation of the fourth dimension or hyperbolic space, the first thing I do is pull out some of Henry Segerman''s sculptures. His book reveals the mathematics of these forms, as well as his deep aesthetic sensibility.
—Vi Hart, mathemusician and virtual reality philosopher

Visual thinkers, rejoice! Three-dimensional shapes have never been so lovingly illustrated. Segerman’s gorgeous 3D printed models, and his equally beautiful explanations, make this book a treat for the right-brained among us.
—Steven Strogatz, Cornell University, author of The Joy of x: A Guided Tour of Math, from One to Infinity

This book truly reaches into the third dimension and makes complex geometrical models easier to understand. As a bonus, it''s closely coupled with an interactive website and the 3D printed models you can access there. Equally valuable for those of us wrapping our heads around 3D printed mathematical objects and for students of symmetry, topology, knot theory, or regular polyhedra.
—Carlo H. Séquin, University of California, Berkeley

Henry Segerman has made a name for himself demystifying advanced mathematics with the help of 3D printed models. Here, he tackles some difficult concepts—from symmetry to curvature to the shadowy world of four-dimensional shapes—with clear, inviting explanations and beautiful 3D printed illustrations.
—Evelyn Lamb, University of Utah, author of Scientific American''s Roots of Unity blog