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The Nature Of The Regular Polyhedra
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Book Synopsis A Geometric Analysis of the Platonic Solids and Other Semi-Regular Polyhedra by : Kenneth J. M. MacLean
Download or read book A Geometric Analysis of the Platonic Solids and Other Semi-Regular Polyhedra written by Kenneth J. M. MacLean and published by Loving Healing Press. This book was released on 2007-01-01 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a meticulous geometric investigation of the five Platonic Solids and five other important polyhedra, as well as reference charts for each solid. (Mathematics)
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.
Book Synopsis Shaping Space by : Marjorie Senechal
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 341 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.
Book Synopsis The Nature of the Regular Polyhedra by : Frederick H. Young
Download or read book The Nature of the Regular Polyhedra written by Frederick H. Young and published by . This book was released on 1961 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Convex Polyhedra with Regular Faces by : Viktor A. Zalgaller
Download or read book Convex Polyhedra with Regular Faces written by Viktor A. Zalgaller and published by Springer. This book was released on 1969 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Geometric Analysis of the Platonic Solids and Other Semi-Regular Polyhedra by : Kenneth J. M. MacLean
Download or read book A Geometric Analysis of the Platonic Solids and Other Semi-Regular Polyhedra written by Kenneth J. M. MacLean and published by Loving Healing Press. This book was released on 2015-06-01 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Getting Inside the Mind of Nature: Discover the simple but powerful mathematics of the underlying geometric figures that shape our world Can geometry be exciting? It can for those who can appreciate the beauty of numbers and their relationships. This book contains a meticulous geometric investigation of the 5 Platonic Solids and 5 other important polyhedra, as well as reference charts for each solid. Poly (many) hedron (face) means "many faces." Polyhedra are 3 dimensional figures with 4 or more faces, or sides. These polyhedra are reflections of Nature herself, and a study of them provides insight into the way the world is structured. Nature is not only beautiful, but highly intelligent. As you explore the polyhedra in this book, this will become apparent over and over again. The book contains a geometric explanation of the Phi Ratio and Fibonacci series, and a detailed analysis of the pentagon, which forms the basis for many of these solids. The pentagon is composed entirely of Phi relationships, and is integral to a proper understanding of sacred geometry. With over 140 full-color illustrations, this book is perfect for teachers and students of geometry alike. It is a must for those who are serious about sacred geometry. This book is dedicated to those who can appreciate the logic of numbers and the beauty of nature, for they are both aspects of the same unifying principle. Prerequisites: knowledge of simple algebra and elementary trigonometry. No brainiac math skills required! Only the ability to appreciate nature's own logic. Book #1 in the Geometric Explorations Series From Loving Healing Press (www.LovingHealing.com)
Book Synopsis Polyhedron Models by : Magnus J. Wenninger
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 Euler's Gem written by David S. Richeson and published by Princeton University Press. This book was released on 2019-07-23 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: How a simple equation reshaped mathematics Leonhard Euler’s polyhedron formula describes the structure of many objects—from soccer balls and gemstones to Buckminster Fuller’s buildings and giant all-carbon molecules. Yet Euler’s theorem is so simple it can be explained to a child. From ancient Greek geometry to today’s cutting-edge research, Euler’s Gem celebrates the discovery of Euler’s beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. Using wonderful examples and numerous illustrations, David Richeson presents this mathematical idea’s many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who’s who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem’s development, Euler’s Gem will fascinate every mathematics enthusiast. This paperback edition contains a new preface by the author.
Download or read book Platonic & Archimedean Solids written by and published by Bloomsbury Publishing USA. This book was released on 2002-04-01 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: Looks at the relationship between the five Platonic and thirteen Archimedean solids.
Book Synopsis The Secret of the Universe by : Johannes Kepler
Download or read book The Secret of the Universe written by Johannes Kepler and published by . This book was released on 1981 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :C. Edward Sandifer Publisher :The Mathematical Association of America ISBN 13 :0883855844 Total Pages :254 pages Book Rating :4.8/5 (838 download)
Book Synopsis How Euler Did Even More by : C. Edward Sandifer
Download or read book How Euler Did Even More written by C. Edward Sandifer and published by The Mathematical Association of America. This book was released on 2014-11-19 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sandifer has been studying Euler for decades and is one of the world’s leading experts on his work. This volume is the second collection of Sandifer’s “How Euler Did It” columns. Each is a jewel of historical and mathematical exposition. The sum total of years of work and study of the most prolific mathematician of history, this volume will leave you marveling at Euler’s clever inventiveness and Sandifer’s wonderful ability to explicate and put it all in context.
Book Synopsis Shaping Space by : Marjorie Senechal
Download or read book Shaping Space written by Marjorie Senechal and published by Birkhäuser. This book was released on 1988 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Nature of Mathematics and the Mathematics of Nature by : S. Andersson
Download or read book The Nature of Mathematics and the Mathematics of Nature written by S. Andersson and published by Elsevier. This book was released on 1998-10-09 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chemistry, physics and biology are by their nature genuinely difficult. Mathematics, however, is man-made, and therefore not as complicated. Two ideas form the basis for this book: 1) to use ordinary mathematics to describe the simplicity in the structure of mathematics and 2) to develop new branches of mathematics to describe natural sciences. Mathematics can be described as the addition, subtraction or multiplication of planes. Using the exponential scale the authors show that the addition of planes gives the polyhedra, or any solid. The substraction of planes gives saddles. The multiplication of planes gives the general saddle equations and the multispirals. The equation of symmetry is derived, which contains the exponential scale with its functions for solids, the complex exponentials with the nodal surfaces, and the GD (Gauss Distribution) mathematics with finite periodicity. Piece by piece, the authors have found mathematical functions for the geometrical descriptions of chemical structures and the structure building operations. Using the mathematics for dilatation; twins, trillings, fourlings and sixlings are made, and using GD mathematics these are made periodic. This description of a structure is the nature of mathematics itself. Crystal structures and 3D mathematics are synonyms. Mathematics are used to describe rod packings, Olympic rings and defects in solids. Giant molecules such as cubosomes, the DNA double helix, and certain building blocks in protein structures are also described mathematically.
Book Synopsis Groups and Symmetry by : Bijan Davvaz
Download or read book Groups and Symmetry written by Bijan Davvaz and published by Springer Nature. This book was released on 2021-11-17 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a readable account of the examples and fundamental results of groups from a theoretical and geometrical point of view. This is the second book of the set of two books on groups theory. Topics on linear transformation and linear groups, group actions on sets, Sylow’s theorem, simple groups, products of groups, normal series, free groups, platonic solids, Frieze and wallpaper symmetry groups and characters of groups have been discussed in depth. Covering all major topics, this book is targeted to advanced undergraduate students of mathematics with no prerequisite knowledge of the discussed topics. Each section ends with a set of worked-out problems and supplementary exercises to challenge the knowledge and ability of the reader.
Book Synopsis Structure in Nature Is a Strategy for Design by : Peter Pearce
Download or read book Structure in Nature Is a Strategy for Design written by Peter Pearce and published by MIT Press. This book was released on 1990 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The structural designs that occur in nature - in molecules, in crystals, in living cells - appear in this fully illustrated book as a source of inspiration and study of design of man-made structures" -- BOOK JACKET.
Book Synopsis The Essence of Mathematics Through Elementary Problems by : Alexandre Borovik
Download or read book The Essence of Mathematics Through Elementary Problems written by Alexandre Borovik and published by . This book was released on 2019-06-11 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Computational Origami by : Ryuhei Uehara
Download or read book Introduction to Computational Origami written by Ryuhei Uehara and published by Springer Nature. This book was released on 2020-06-29 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on origami from the point of view of computer science. Ranging from basic theorems to the latest research results, the book introduces the considerably new and fertile research field of computational origami as computer science. Part I introduces basic knowledge of the geometry of development, also called a net, of a solid. Part II further details the topic of nets. In the science of nets, there are numerous unresolved issues, and mathematical characterization and the development of efficient algorithms by computer are closely connected with each other. Part III discusses folding models and their computational complexity. When a folding model is fixed, to find efficient ways of folding is to propose efficient algorithms. If this is difficult, it is intractable in terms of computational complexity. This is, precisely, an area for computer science research. Part IV presents some of the latest research topics as advanced problems. Commentaries on all exercises included in the last chapter. The contents are organized in a self-contained way, and no previous knowledge is required. This book is suitable for undergraduate, graduate, and even high school students, as well as researchers and engineers interested in origami.
