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Visualizing Mathematics with 3D Printing

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,, 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.
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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. Sequin, 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 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, Author of The Joy of x: A Guided Tour of Math, from One to Infinity 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

Table of Contents

PrefaceAcknowledgments1. Symmetry2. Polyhedra3. Four-Dimensional Space4. Tilings and Curvature5. Knots6. Surfaces7. MenagerieAppendix AAppendix BIndex

About the Author

Henry Segerman is one of the leading figures in the new world of math and 3D printing. He is an assistant professor of mathematics at Oklahoma State University.


My best advice is to go out and buy yourself a copy of the book. * Chalkdust Magazine * The breadth of Segerman's 3D printing explorations is impressive. Coupled with the clarity of his explanations of the mathematics behind those explorations, this book becomes an easy recommendation for any reader interested in learning some beautiful mathematical ideas. * Journal of Mathematics and the Arts * No previous mathematical maturity is required. The work is a good addition to any academic library. Highly recommended * Choice * I have great difficulty thinking about Visualizing Mathematics with 3D Printing as "just a book." The careful choice, quality and effectiveness of the 140+ images in the book is outstanding. What Segerman has developed is much bigger than a book; he has developed a whole platform to complement the book and explore mathematical concepts. Visualizing Mathematics with 3D printing allows the reader to manipulate with a computer or 3D print the objects discussed, making it possible to physically interact with the concepts. * Mathematical Association of America * ... this book serves as a launching point for teachers who are interested in exploring more advanced geometries or topology themselves. It could also guide conversations between STEM and arts educators trying to build an integrated learning experience. * National Council of Teachers of Mathematics *

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