Download or read book Polyhedra written by Peter R. Cromwell and published by Cambridge University Press. This book was released on 1997 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polyhedra have cropped up in many different guises throughout recorded history. In modern times, polyhedra and their symmetries have been cast in a new light by combinatorics an d group theory. This book comprehensively documents the many and varied ways that polyhedra have come to the fore throughout the development of mathematics. The author strikes a balance between covering the historical development of the theory surrounding polyhedra, and presenting a rigorous treatment of the mathematics involved. It is attractively illustrated with dozens of diagrams to illustrate ideas that might otherwise prove difficult to grasp. Historians of mathematics, as well as those more interested in the mathematics itself, will find this unique book fascinating.
Download or read book Convex Polyhedra written by A.D. Alexandrov and published by Springer Science & Business Media. This book was released on 2005-12-08 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic geometry text explores the theory of 3-dimensional convex polyhedra in a unique fashion, with exceptional detail. Vital and clearly written, the book includes the basics of convex polyhedra and collects the most general existence theorems for convex polyhedra that are proved by a new and unified method. This edition includes a comprehensive bibliography by V.A. Zalgaller, and related papers as supplements to the original text.
Download or read book Polyhedra written by Anthony Pugh and published by Univ of California Press. This book was released on 1976 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Polyhedron Models written by Magnus J. Wenninger and published by Cambridge University Press. This book was released on 1971 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: he author describes simply and carefully how to make models of all the known uniform polyhedra and some of the stellated forms.
Download or read book Descartes on Polyhedra written by P. J. Federico and published by Springer Science & Business Media. This book was released on 1982-12 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present essay stems from a history of polyhedra from 1750 to 1866 written several years ago (as part of a more general work, not published). So many contradictory statements regarding a Descartes manuscript and Euler, by various mathematicians and historians of mathematics, were encountered that it was decided to write a separate study of the relevant part of the Descartes manuscript on polyhedra. The contemplated short paper grew in size, as only a detailed treatment could be of any value. After it was completed it became evident that the entire manuscript should be treated and the work grew some more. The result presented here is, I hope, a complete, accurate, and fair treatment of the entire manuscript. While some views and conclusions are expressed, this is only done with the facts before the reader, who may draw his or her own conclusions. I would like to express my appreciation to Professors H. S. M. Coxeter, Branko Griinbaum, Morris Kline, and Dr. Heinz-Jiirgen Hess for reading the manuscript and for their encouragement and suggestions. I am especially indebted to Dr. Hess, of the Leibniz-Archiv, for his assistance in connection with the manuscript. I have been greatly helped in preparing the translation ofthe manuscript by the collaboration of a Latin scholar, Mr. Alfredo DeBarbieri. The aid of librarians is indispensable, and I am indebted to a number of them, in this country and abroad, for locating material and supplying copies.
Download or read book Build Your Own Polyhedra written by Peter Hilton and published by Addison Wesley Publishing Company. This book was released on 1994 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Demonstrates the properties of geometrical structures by showing how to buid three-dimensional shapes using easily accessible materials.
Download or read book Shaping Space written by Marjorie Senechal and published by Springer Science & Business Media. This book was released on 2013-03-22 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition is based off of the very popular Shaping Space: A Polyhedral Approach, first published twenty years ago. The book is expanded and updated to include new developments, including the revolutions in visualization and model-making that the computer has wrought. Shaping Space is an exuberant, richly-illustrated, interdisciplinary guide to three-dimensional forms, focusing on the suprisingly diverse world of polyhedra. Geometry comes alive in Shaping Space, as a remarkable range of geometric ideas is explored and its centrality in our cultre is persuasively demonstrated. The book is addressed to designers, artists, architects, engineers, chemists, computer scientists, mathematicians, bioscientists, crystallographers, earth scientists, and teachers at all levels—in short, to all scholars and educators interested in, and working with, two- and three-dimensinal structures and patterns.
Download or read book The Complete Book of Origami Polyhedra written by Tomoko Fuse and published by Tuttle Publishing. This book was released on 2021-10-12 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learn to fold incredible geometric origami models from "The Queen of Modular Origami!" In this book, Tomoko Fuse--Japan's most famous living origami artist--shows you how to create amazing polyhedral models using the techniques of modular origami (where many paper sheets are folded then locked together without glue or tape). Make 64 intriguing modular models, including: Stackable Modules--The perfect starting point for novices, these simple constructions result in stunning three-dimensional forms 3-D Stars--Dazzling decorative starbursts that look great on a Christmas tree, on your mantle--or even in an art gallery Manifold Modulars--"Inception-like" models in which individual modular constructions themselves become modules within a larger piece Cubes and Boxes--Perfect for gift giving--and there is no finer teacher for these than renowned origami box specialist Tomoko Fuse And many more! *Recommended for experienced folders and up*
Download or read book Geometric Folding Algorithms written by Erik D. Demaine and published by Cambridge University Press. This book was released on 2007-07-16 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Did you know that any straight-line drawing on paper can be folded so that the complete drawing can be cut out with one straight scissors cut? That there is a planar linkage that can trace out any algebraic curve, or even 'sign your name'? Or that a 'Latin cross' unfolding of a cube can be refolded to 23 different convex polyhedra? Over the past decade, there has been a surge of interest in such problems, with applications ranging from robotics to protein folding. With an emphasis on algorithmic or computational aspects, this treatment gives hundreds of results and over 60 unsolved 'open problems' to inspire further research. The authors cover one-dimensional (1D) objects (linkages), 2D objects (paper), and 3D objects (polyhedra). Aimed at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from school students to researchers.
Download or read book Convex Polyhedra written by A.D. Alexandrov and published by Springer Science & Business Media. This book was released on 2005-02-10 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic geometry text explores the theory of 3-dimensional convex polyhedra in a unique fashion, with exceptional detail. Vital and clearly written, the book includes the basics of convex polyhedra and collects the most general existence theorems for convex polyhedra that are proved by a new and unified method. This edition includes a comprehensive bibliography by V.A. Zalgaller, and related papers as supplements to the original text.
Download or read book Folding Polyhedra written by Alexander Heinz and published by . This book was released on 2021-05-28 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explore the reaches of your imagination by combining art, craft, and mathematics to create the age-old geometric form of the polyhedra. More than 50 projects use just one center point to create shapes that are folded symmetrically and build upon each other. With easy-to-follow, step-by-step instructions, you can construct models from regular polygons, including equilateral triangles, squares, pentagons, hexagons, octagons, and decagons. These engaging projects require active, mental participation and can aid in reshaping familiar thought patterns as well as keeping your focus on the present moment as a form of relaxation. Also included is a wealth of detail on the subject of geometry. Once a requirement for entry into the philosopher Plato's Academy, now geometry can be enjoyed by everyone with an eye for fun. The book includes a chapter of tips to create your own designs.
Download or read book Beginner s Book of Modular Origami Polyhedra written by Rona Gurkewitz and published by Courier Corporation. This book was released on 2012-03-07 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt: This manual features 17 easy-to-master projects involving the Platonic solids: the tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron. Includes detailed diagrams and photos of all the completed models.
Download or read book Polyhedra Primer written by Peter Jon Pearce and published by CreateSpace. This book was released on 2015-02-03 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is a lucid thoughtful guide to understanding the structure and organization of three-dimension al space. In 250 captioned drawings this book brilliantly communicates the beauty and geometry of polyhedra. Beginning with polygons and tessellations. It proceeds in a logical sequence to finite polyhedra, dual polyhedra, space filling, and open packings. Important considerations of symmetry, periodic and uniform patterns, and regular and semiregular forms are presented. Because the understanding of polyhedra is enhanced by the manipulation of models, a chapter on both two- and three-dimensional constructions is included. This uniquely valuable reference work will be welcomed by designers, architects, mathematicians, and scientists who are interested in a graphic, yet rigorous, presentation of form and spatlal options. This little book will be a delightful addition to the libraries of those readers who are entranced by the intriguing subject of polyhedra.
Download or read book A Plethora of Polyhedra in Origami written by John Montroll and published by Courier Corporation. This book was released on 2002-01-01 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: Step-by-step instructions and 970 clear diagrams show beginning and experienced paperfolders how to create 27 amazing polyhedra from one sheet of paper. Graded according to difficulty, the projects range from a simple cube, tetrahedron and octahedron to a challenging rhombic dodecahedron, sunken icosahedron, and an antidiamond with pentagonal base.
Download or read book Designing and Building Tessellated Polyhedra written by Robert Fathauer and published by Tessellations. This book was released on 2017-08 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polyhedra allow geometric shapes in the plane to become solids in our three-dimensional world. Tessellations in which individual tiles are lifelike motifs are a fun combination of art and mathematics. Designing and Building Tessellated Polyhedra brings these two fascinating topics together a for hands-on learning experience rich in math content. Nets for 24 different polyhedra, including all of the Platonic and Archimedean solids, are presented both with and without tessellations applied to them. This allows polyhedra to be built with ready-made designs that can be colored if desired, or printed in beautiful color using the included CD. Another option is building undecorated polyhedra that have the names and key properties printed on them. Yet another possibility is to use templates to design new tessellations that can be applied to the polyhedra. The book also contains background on polyhedra and templates for tessellated cones, cylinders, and Msbius strips. For classroom use, ten activities with worksheets, designed to address ten different specific Common Core State Standards for Mathematics are included as well. Ages 12-17
Download or read book Integer Points in Polyhedra written by Alexander Barvinok and published by European Mathematical Society. This book was released on 2008 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a self-contained exposition of several core aspects of the theory of rational polyhedra with a view towards algorithmic applications to efficient counting of integer points, a problem arising in many areas of pure and applied mathematics. The approach is based on the consistent development and application of the apparatus of generating functions and the algebra of polyhedra. Topics range from classical, such as the Euler characteristic, continued fractions, Ehrhart polynomial, Minkowski Convex Body Theorem, and the Lenstra-Lenstra-Lovasz lattice reduction algorithm, to recent advances such as the Berline-Vergne local formula. The text is intended for graduate students and researchers. Prerequisites are a modest background in linear algebra and analysis as well as some general mathematical maturity. Numerous figures, exercises of varying degree of difficulty as well as references to the literature and publicly available software make the text suitable for a graduate course.
Download or read book Compound Polyhedra written by Fergus Currie and published by Tarquin Group. This book was released on 2021-10-11 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: A book of ten geometric models of advanced modular origami designed by Fergus Currie with full instructions and diagrams on how to make the following: 1. Compound of Cube and Octahedron 2. Compound of Icosahedron and Dodecahedron 3. The Small Triambic Icosahedron 4. Compound of Small Triambic Icosahedron and Dodechedron 5. Left Pentagonal Icosatetrahedron 6. Compound of Left and Right Pentagonal Icosatetrahedra 7. Compound of Three Cubes 8. Compound of Three Tetrahedra 9. Compound of Five Octahedra 10. Wire-frame model of Compound of Two Tetrahedra It also includes an introduction with sections on the mathematics behind the models; a short history of modular origami; a section on tools and folding techniques, and a gallery of the finished models that are presented in the book.
