Treks into Intuitive Geometry

The World of Polygons and Polyhedra

Author: Jin Akiyama,Kiyoko Matsunaga

Publisher: Springer

ISBN: 4431558438

Category: Mathematics

Page: 425

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This book is written in a style that uncovers the mathematical theories buried in our everyday lives such as examples from patterns that appear in nature, art, and traditional crafts, and in mathematical mechanisms in techniques used by architects. The authors believe that through dialogues between students and mathematicians, readers may discover the processes by which the founders of the theories came to their various conclusions―their trials, errors, tribulations, and triumphs. The goal is for readers to refine their mathematical sense of how to find good questions and how to grapple with these problems. Another aim is to provide enjoyment in the process of applying mathematical rules to beautiful art and design by examples that highlight the wonders and mysteries from our daily lives. To fulfill these aims, this book deals with the latest unique and beautiful results in polygons and polyhedra and the dynamism of geometrical research history that can be found around us. The term "intuitive geometry" was coined by Lászlo Fejes Tóth to refer to the kind of geometry which, in Hilbert's words, can be explained to and appeal to the "man on the street." This book allows people to enjoy intuitive geometry informally and instinctively. It does not require more than a high school level of knowledge but calls for a sense of wonder, intuition, and mathematical maturity.

Platonic & Archimedean Solids

Author: Daud Sutton

Publisher: Bloomsbury Publishing USA

ISBN: 0802713866

Category: Mathematics

Page: 58

View: 7523

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Looks at the relationship between the five Platonic and thirteen Archimedean solids.

A Mathematical Space Odyssey

Solid Geometry in the 21st Century

Author: Claudi Alsina,Roger B. Nelsen

Publisher: The Mathematical Association of America

ISBN: 0883853582

Category: Mathematics

Page: 288

View: 8825

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Solid geometry is the traditional name for what we call today the geometry of three-dimensional Euclidean space. Courses in solid geometry have largely disappeared from American high schools and colleges. The authors are convinced that a mathematical exploration of three-dimensional geometry merits some attention in today’s curriculum. A Mathematical Space Odyssey: Solid Geometry in the 21st Century is devoted to presenting techniques for proving a variety of mathematical results in three-dimensional space, techniques that may improve one’s ability to think visually. Special attention is given to the classical icons of solid geometry (prisms, pyramids, platonic solids, cones, cylinders, and spheres) and many new and classical results: Cavalieri’s principle, Commandino’s theorem, de Gua’s theorem, Prince Rupert’s cube, the Menger sponge, the Schwarz lantern, Euler’s rotation theorem, the Loomis-Whitney inequality, Pythagorean theorems in three dimensions, etc. The authors devote a chapter to each of the following basic techniques for exploring space and proving theorems: enumeration, representation, dissection, plane sections, intersection, iteration, motion, projection, and folding and unfolding. In addition to many figures illustrating theorems and their proofs, a selection of photographs of three-dimensional works of art and architecture are included. Each chapter includes a selection of Challenges for the reader to explore further properties and applications. It concludes with solutions to all the Challenges in the book, references, and a complete index. Readers should be familiar with high school algebra, plane and analytic geometry, and trigonometry. While brief appearances of calculus do occur, no knowledge of calculus is necessary to enjoy this book.

The Wonders of Physics

Third Edition

Author: Andrey Varlamov,Lev Aslamazov

Publisher: World Scientific Publishing Company

ISBN: 9813108274

Category: Science

Page: 328

View: 9621

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The book in your hands develops the best traditions of Russian scientific popular literature. Written in a clear and captivating manner by working theoretical physicists, who are, at the same time, dedicated popularizers of scientific knowledge, it brings to the reader the latest achievements in quantum solid-state physics, but along the way also shows how the laws of physics reveal themselves even in seemingly trivial episodes concerning the natural phenomena around us. Most importantly, it shows that we live in a world where scientists are capable of “proving harmony with algebra”. — A A Abrikosov, 2003 Nobel Prize Winner in Physics The third edition is considerably extended with three new chapters where the author discusses exciting examples of applications of recent achievements of physics in medicine, nanotechnologies, and physics in cuisine.

Trigger Happy

Author: Steven Poole

Publisher: Skyhorse Publishing, Inc.

ISBN: 162872224X

Category: Games & Activities

Page: 999

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The Edge calls Trigger Happy a "seminal piece of work." For the first time ever, an aficionado with a knowledge of art, culture, and a real love of gaming takes a critical look at the future of our videogames, and compares their aesthetic and economic impact on society to that of film. Thirty years after the invention of the simplest of games, more videogames are played by adults than children. This revolutionary book is the first-ever academically worthy and deeply engaging critique of one of today's most popular forms of play: videogames are on track to supersede movies as the most innovative form of entertainment in the new century.


Notes, Problems and Exercises

Author: Roger Delbourgo

Publisher: World Scientific Publishing Company

ISBN: 9813203137


Page: 188

View: 7261

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This book provides a thorough, intermediate-level yet concise course in Trigonometry for use in colleges. There are 37 short chapters, each treating one specific theme and containing worked examples and easy exercises. Central to the work are the trigonometric properties of triangle ABC and its associated points. A small appendix contains some Spherical Trigonometry with interesting problems related to the earth; a larger one for enthusiastic students provides further lengthier exercises for extra practice, and full solutions are supplied in the conclusion. Compared with other books on Trigonometry, this book covers the vast spread of topics. Especially, the author reminds readers of the historical importance of theorems enunciated by such contributors as Ptolemy, Euler, Morley, etc. Their names not only invite the readers to appreciate the beauty of these results, but also direct readers to mystery unknown. Request Inspection Copy

The Pursuit of Destiny

A History of Prediction

Author: Paul Halpern

Publisher: Perseus Books Group


Category: Science

Page: 250

View: 7856

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The physicist-author of The Cyclical Serpent traces the history of forecasting from its mystical origins to its evolution as a modern science, drawing on the latest theories of complexity, chaos theory, quantum theory, and relativity to describe the latest methods of scientific, social, and technological forecasting. 15,000 first printing.


60 Tips, Tricks, and Games to Take Your Mind to the Next Level

Author: Ron Hale-Evans,Marty Hale-Evans

Publisher: John Wiley & Sons

ISBN: 1118166434

Category: Computers

Page: 408

View: 4199

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Compelling tips and tricks to improve your mental skills Don't you wish you were just a little smarter? Ron and Marty Hale-Evans can help with a vast array of witty, practical techniques that tune your brain to peak performance. Founded in current research, Mindhacker features 60 tips, tricks, and games to develop your mental potential. This accessible compilation helps improve memory, accelerate learning, manage time, spark creativity, hone math and logic skills, communicate better, think more clearly, and keep your mind strong and flexible.

The Sleepwalkers

A History of Man's Changing Vision of the Universe

Author: Arthur Koestler

Publisher: Penguin UK

ISBN: 0141394544

Category: Fiction

Page: 624

View: 3914

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Arthur Koestler's extraordinary history of humanity's changing vision of the universe In this masterly synthesis, Arthur Koestler cuts through the sterile distinction between 'sciences' and 'humanities' to bring to life the whole history of cosmology from the Babylonians to Newton. He shows how the tragic split between science and religion arose and how, in particular, the modern world-view replaced the medieval world-view in the scientific revolution of the seventeenth century. He also provides vivid and judicious pen-portraits of a string of great scientists and makes clear the role that political bias and unconscious prejudice played in their creativity.

Factors and Factorizations of Graphs

Proof Techniques in Factor Theory

Author: Jin Akiyama,Mikio Kano

Publisher: Springer Science & Business Media

ISBN: 3642219187

Category: Computers

Page: 353

View: 5275

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This book chronicles the development of graph factors and factorizations. It pursues a comprehensive approach, addressing most of the important results from hundreds of findings over the last century. One of the main themes is the observation that many theorems can be proved using only a few standard proof techniques. This stands in marked contrast to the seemingly countless, complex proof techniques offered by the extant body of papers and books. In addition to covering the history and development of this area, the book offers conjectures and discusses open problems. It also includes numerous explanatory figures that enable readers to progressively and intuitively understand the most important notions and proofs in the area of factors and factorization.

Error-Correcting Linear Codes

Classification by Isometry and Applications

Author: Anton Betten,Michael Braun,Harald Fripertinger,Adalbert Kerber,Axel Kohnert,Alfred Wassermann

Publisher: Springer Science & Business Media

ISBN: 3540317031

Category: Mathematics

Page: 798

View: 6074

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This text offers an introduction to error-correcting linear codes for researchers and graduate students in mathematics, computer science and engineering. The book differs from other standard texts in its emphasis on the classification of codes by means of isometry classes. The relevant algebraic are developed rigorously. Cyclic codes are discussed in great detail. In the last four chapters these isometry classes are enumerated, and representatives are constructed algorithmically.

Advanced RenderMan

Creating CGI for Motion Pictures

Author: Anthony A. Apodaca,Larry Gritz,Ronen Barzel

Publisher: Morgan Kaufmann

ISBN: 9781558606180

Category: Computers

Page: 544

View: 8745

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Advanced RenderMan: Creating CGI for Motion Pictures is precisely what you and other RenderMan users are dying for. Written by the world's foremost RenderMan experts, it offers thoroughly updated coverage of the standard while moving beyond the scope of the original RenderMan Companion to provide in-depth information on dozens of advanced topics. Both a reference and a tutorial, this book will quickly prove indispensable, whether you're a technical director, graphics programmer, modeler, animator, or hobbyist. Explore the Power of RenderMan * Use the entire range of geometric primitives supported by RenderMan. * Understand how and when to use procedural primitives and level of detail. * Master every nuance of the Shading Language. * Write detailed procedural shaders using texture, displacement, pattern generation, and custom reflection models. * Write shaders for special effects relating to volumes, custom lighting, and non-photorealistic media. * Use antialiasing to ensure that your shaders are free of artifacts. * Minimize the expense of rendering scenes by optimizing input. Other Features from Advanced RenderMan * Offers expert advice and instruction applicable to any RenderMan-compliant renderer. * Filled with technical illustrations and many full-color representations of effects supported by the RenderMan standard. * Includes a chapter reviewing key math and computer graphics concepts.

The Ancient Secret of the Flower of Life, Volume 1

Author: Drunvalo Melchizedek

Publisher: Light Technology Publishing


Category: Life

Page: 228

View: 2955

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"Here, Drunvalo Melchizedek presents in text and graphics the first half of the Flower of Life Workshop, illuminating the mysteries of how we came to be, why the world is the way it is and the subtle energies that allow our awareness to blossom into its true beauty." --COVER.

Fun with Algorithms

6th International Conference, FUN 2012, Venice, Italy, June 4-6, 2012, Proceedings

Author: Evangelos Kranakis,DANNY KRIZANC,Flaminia Luccio

Publisher: Springer

ISBN: 3642303471

Category: Computers

Page: 397

View: 7791

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This book constitutes the refereed proceedings of the 6th International Conference, FUN 2012, held in June 2012 in Venice, Italy. The 34 revised full papers were carefully reviewed and selected from 56 submissions. They feature a large variety of topics in the field of the use, design, and analysis of algorithms and data structures, focusing on results that provide amusing, witty but nonetheless original and scientifically profound contributions to the area.

Nature of Mathematics

Author: Karl J. Smith

Publisher: Cengage Learning

ISBN: 1305855582

Category: Mathematics

Page: 1024

View: 5008

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Written for liberal arts students and based on the belief that learning to solve problems is the principal reason for studying mathematics, Karl Smith introduces students to Polya’s problem-solving techniques and shows them how to use these techniques to solve unfamiliar problems that they encounter in their own lives. Through the emphasis on problem solving and estimation, along with numerous in-text study aids, students are assisted in understanding the concepts and mastering the techniques. In addition to the problem-solving emphasis, THE NATURE OF MATHEMATICS is renowned for its clear writing, coverage of historical topics, selection of topics, level, and excellent applications problems. Smith includes material on such practical real-world topics as finances (e.g. amortization, installment buying, annuities) and voting and apportionment. With the help of this text, thousands of students have experienced mathematics rather than just do problems--and benefited from a writing style that boosts their confidence and fosters their ability to use mathematics effectively in their everyday lives. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

The Handy Math Answer Book

Author: Patricia Barnes-Svarney,Thomas E Svarney

Publisher: Visible Ink Press

ISBN: 1578593867

Category: Mathematics

Page: 528

View: 2129

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From modern-day challenges such as balancing a checkbook, following the stock market, buying a home, and figuring out credit card finance charges to appreciating historical developments by Pythagoras, Archimedes, Newton, and other mathematicians, this engaging resource addresses more than 1,000 questions related to mathematics. Organized into chapters that cluster similar topics in an easily accessible format, this reference provides clear and concise explanations about the fundamentals of algebra, calculus, geometry, trigonometry, and other branches of mathematics. It contains the latest mathematical discoveries, including newly uncovered historical documents and updates on how science continues to use math to make cutting-edge innovations in DNA sequencing, superstring theory, robotics, and computers. With fun math facts and illuminating figures, The Handy Math Answer Book explores the uses of math in everyday life and helps the mathematically challenged better understand and enjoy the magic of numbers.

Mathematics in Everyday Life

Author: John Haigh

Publisher: Springer

ISBN: 3319279394

Category: Mathematics

Page: 159

View: 5717

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How does mathematics impact everyday events? The purpose of this book is to show a range of examples where mathematics can be seen at work in everyday life. From money (APR, mortgage repayments, personal finance), simple first and second order ODEs, sport and games (tennis, rugby, athletics, darts, tournament design, soccer, snooker), business (stock control, linear programming, check digits, promotion policies, investment), the social sciences (voting methods, Simpson’s Paradox, drug testing, measurements of inequality) to TV game shows and even gambling (lotteries, roulette, poker, horse racing), the mathematics behind commonplace events is explored. Fully worked examples illustrate the ideas discussed and each chapter ends with a collection of exercises. Everyday Mathematics supports other first year modules by giving students extra practice in working with calculus, linear algebra, geometry, trigonometry and probability. Secondary/high school level mathematics is all that is required for students to understand the material. Those students whose degree course includes writing an extended mathematical essay will find many suitable topics here, with pointers to extend and develop the material.