Download Free How To Fold It The Mathematics Of Linkages Origami And Polyhedra Book in PDF and EPUB Free Download. You can read online How To Fold It The Mathematics Of Linkages Origami And Polyhedra and write the review.

What do proteins and pop-up cards have in common? How is opening a grocery bag different from opening a gift box? How can you cut out the letters for a whole word all at once with one straight scissors cut? How many ways are there to flatten a cube? With the help of 200 colour figures, author Joseph O'Rourke explains these fascinating folding problems starting from high school algebra and geometry and introducing more advanced concepts in tangible contexts as they arise. He shows how variations on these basic problems lead directly to the frontiers of current mathematical research and offers ten accessible unsolved problems for the enterprising reader. Before tackling these, you can test your skills on fifty exercises with complete solutions. The book's website,, has dynamic animations of many of the foldings and downloadable templates for readers to fold or cut out.
How can linkages, pieces of paper, and polyhedra be folded? The authors present hundreds of results and over 60 unsolved 'open problems' in this comprehensive look at the mathematics of folding, with an emphasis on algorithmic or computational aspects. Folding and unfolding problems have been implicit since Albrecht Dürer in the early 1500s, but have only recently been studied in the mathematical literature. Over the past decade, there has been a surge of interest in these problems, with applications ranging from robotics to protein folding. A proof shows that it is possible to design a series of jointed bars moving only in a flat plane that can sign a name or trace any other algebraic curve. One remarkable algorithm shows you can fold any straight-line drawing on paper so that the complete drawing can be cut out with one straight scissors cut. Aimed primarily at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from high school students to researchers.
Project Origami: Activities for Exploring Mathematics, Second Edition presents a flexible, discovery-based approach to learning origami-math topics. It helps readers see how origami intersects a variety of mathematical topics, from the more obvious realm of geometry to the fields of algebra, number theory, and combinatorics. With over 100 new pages, this updated and expanded edition now includes 30 activities and offers better solutions and teaching tips for all activities. The book contains detailed plans for 30 hands-on, scalable origami activities. Each activity lists courses in which the activity might fit, includes handouts for classroom use, and provides notes for instructors on solutions, how the handouts can be used, and other pedagogical suggestions. The handouts are also available on the book’s CRC Press web page. Reflecting feedback from teachers and students who have used the book, this classroom-tested text provides an easy and entertaining way for teachers to incorporate origami into a range of college and advanced high school math courses. Visit the author’s website for more information.
The book contains papers from the proceedings of the 3rd International Meeting of Origami Science, Math, and Education, sponsored by OrigamiUSA. They cover topics ranging from the mathematics of origami using polygon constructions and geometric projections, applications, and science of origami, and the use of origami in education.
Unfolding Mathematics With Unit Origami At last-an origami book designed specifically for mathematics classrooms! Origami books are typically written by origami experts and aimed at origami enthusiasts. This art form lends itself wonderfully to teaching mathematicsbut it's been up to you to find ways to do it. Now comes Unfolding Mathematics with Unit Origami, designed especially for algebra and geometry students in high school or middle school. Its elegant illustrations and detailed folding and assembly instructions enable you and your students to create beautiful and intriguing three-dimensional origami models. Its 16 absorbing activitiesall in blackline master formhave been carefully prepared in order of increasing difficulty of both folds and mathematical concepts. Through origami folding sequences, basic mathematical ideas reveal themselves: algebraic and angle relationships and different types of symmetry in two and three dimensions will engage your students'interest in new ways. You can choose activities from anywhere in the book, but if you move from front to back you'll cover an amazingly broad range of mathematical topics. And while the book's purpose is to teach mathematics, it also introduces students to the art of origami and contributions made to that art by noted origami experts, such as Tomoko Fus, Kunihiko Kasahara, David Masunaga, and Robert Neale. Most activities can be done in one class period and offer opportunities for group work, journal writing, and projects. Autobiographical vignettes by origami artists introduce students to origami culture and prompt students to discuss their own experiences with origami. The overview explains how you can best use this book in your classroom, including methods for assessing student work. Every activity gives you teaching ideas and strategies, as well as suggestions for extensions of the activity. There's also a glossary of terms and a list of recommended readings.
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also features numerous exercises and unsolved problems. The essential introduction to discrete and computational geometry Covers traditional topics as well as new and advanced material Features numerous full-color illustrations, exercises, and unsolved problems Suitable for sophomores in mathematics, computer science, engineering, or physics Rigorous but accessible An online solutions manual is available (for teachers only). To obtain access, please e-mail: [email protected]

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