Visualizing Mathematics with 3D Printing

2016-10-04
Visualizing Mathematics with 3D Printing
Author: Henry Segerman
Publisher: JHU Press
Total Pages: 201
Release: 2016-10-04
Genre: Mathematics
ISBN: 1421420368
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The first book to explain mathematics using 3D printed models. Winner of the Technical Text of the Washington Publishers 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.

Visualizing Mathematics with 3D Printing

2016-10-04
Visualizing Mathematics with 3D Printing
Author: Henry Segerman
Publisher: JHU Press
Total Pages: 201
Release: 2016-10-04
Genre: Computers
ISBN: 142142035X
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The first book to explain mathematics using 3D printed models. Winner of the Technical Text of the Washington Publishers 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.

Illustrating Mathematics

2020-10-16
Illustrating Mathematics
Author: Diana Davis
Publisher: American Mathematical Soc.
Total Pages: 90
Release: 2020-10-16
Genre: Education
ISBN: 1470461226
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This book is for anyone who wishes to illustrate their mathematical ideas, which in our experience means everyone. It is organized by material, rather than by subject area, and purposefully emphasizes the process of creating things, including discussions of failures that occurred along the way. As a result, the reader can learn from the experiences of those who came before, and will be inspired to create their own illustrations. Topics illustrated within include prime numbers, fractals, the Klein bottle, Borromean rings, tilings, space-filling curves, knot theory, billiards, complex dynamics, algebraic surfaces, groups and prime ideals, the Riemann zeta function, quadratic fields, hyperbolic space, and hyperbolic 3-manifolds. Everyone who opens this book should find a type of mathematics with which they identify. Each contributor explains the mathematics behind their illustration at an accessible level, so that all readers can appreciate the beauty of both the object itself and the mathematics behind it.

3D Computer Graphics

2003-05-19
3D Computer Graphics
Author: Samuel R. Buss
Publisher: Cambridge University Press
Total Pages: 397
Release: 2003-05-19
Genre: Computers
ISBN: 1139440381
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This textbook, first published in 2003, emphasises the fundamentals and the mathematics underlying computer graphics. The minimal prerequisites, a basic knowledge of calculus and vectors plus some programming experience in C or C++, make the book suitable for self study or for use as an advanced undergraduate or introductory graduate text. The author gives a thorough treatment of transformations and viewing, lighting and shading models, interpolation and averaging, Bézier curves and B-splines, ray tracing and radiosity, and intersection testing with rays. Additional topics, covered in less depth, include texture mapping and colour theory. The book covers some aspects of animation, including quaternions, orientation, and inverse kinematics, and includes source code for a Ray Tracing software package. The book is intended for use along with any OpenGL programming book, but the crucial features of OpenGL are briefly covered to help readers get up to speed. Accompanying software is available freely from the book's web site.

Visualizing Quaternions

2006-02-06
Visualizing Quaternions
Author: Andrew J. Hanson
Publisher: Elsevier
Total Pages: 530
Release: 2006-02-06
Genre: Mathematics
ISBN: 0080474772
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Introduced 160 years ago as an attempt to generalize complex numbers to higher dimensions, quaternions are now recognized as one of the most important concepts in modern computer graphics. They offer a powerful way to represent rotations and compared to rotation matrices they use less memory, compose faster, and are naturally suited for efficient interpolation of rotations. Despite this, many practitioners have avoided quaternions because of the mathematics used to understand them, hoping that some day a more intuitive description will be available.The wait is over. Andrew Hanson's new book is a fresh perspective on quaternions. The first part of the book focuses on visualizing quaternions to provide the intuition necessary to use them, and includes many illustrative examples to motivate why they are important—a beautiful introduction to those wanting to explore quaternions unencumbered by their mathematical aspects. The second part covers the all-important advanced applications, including quaternion curves, surfaces, and volumes. Finally, for those wanting the full story of the mathematics behind quaternions, there is a gentle introduction to their four-dimensional nature and to Clifford Algebras, the all-encompassing framework for vectors and quaternions. - Richly illustrated introduction for the developer, scientist, engineer, or student in computer graphics, visualization, or entertainment computing. - Covers both non-mathematical and mathematical approaches to quaternions.

Mathematical Reflections

2012-12-06
Mathematical Reflections
Author: Peter Hilton
Publisher: Springer Science & Business Media
Total Pages: 367
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461219329
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A relaxed and informal presentation conveying the joy of mathematical discovery and insight. Frequent questions lead readers to see mathematics as an accessible world of thought, where understanding can turn opaque formulae into beautiful and meaningful ideas. The text presents eight topics that illustrate the unity of mathematical thought as well as the diversity of mathematical ideas. Drawn from both "pure" and "applied" mathematics, they include: spirals in nature and in mathematics; the modern topic of fractals and the ancient topic of Fibonacci numbers; Pascals Triangle and paper folding; modular arithmetic and the arithmetic of the infinite. The final chapter presents some ideas about how mathematics should be done, and hence, how it should be taught. Presenting many recent discoveries that lead to interesting open questions, the book can serve as the main text in courses dealing with contemporary mathematical topics or as enrichment for other courses. It can also be read with pleasure by anyone interested in the intellectually intriguing aspects of mathematics.

Visual Complex Analysis

1997
Visual Complex Analysis
Author: Tristan Needham
Publisher: Oxford University Press
Total Pages: 620
Release: 1997
Genre: Mathematics
ISBN: 9780198534464
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This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.

Pasta by Design

2011
Pasta by Design
Author: George Liaropoulos-Legendre
Publisher:
Total Pages: 0
Release: 2011
Genre: Architectural design
ISBN: 9780500515808
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A mathematical investigation into every known type of pasta.

3D Printed Science Projects

2016-05-11
3D Printed Science Projects
Author: Joan Horvath
Publisher: Apress
Total Pages: 213
Release: 2016-05-11
Genre: Computers
ISBN: 1484213238
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Create 3D printable models that can help students from kindergarten through grad school learn math, physics, botany, chemistry, engineering and more. This book shows parents and teachers how to use the models inside as starting points for 3D printable explorations. Students can start with these models and vary them for their own explorations. Unlike other sets of models that can just be scaled, these models have the science built-in to allow for more insight into the fundamental concepts. Each of the eight topics is designed to be customized by you to create a wide range of projects suitable for science fairs, extra credit, or classroom demonstrations. Science fair project suggestions and extensive "where to learn more" resources are included, too. You will add another dimension to your textbook understanding of science. What You'll Learn Create (and present the science behind) 3D printed models. Use a 3D printer to create those models as simply as possible. Discover new science insights from designing 3D models. Who This Book Is For Parents and teachers