Download or read book Geometry Turned On written by James King and published by Cambridge University Press. This book was released on 1997-10-30 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Articles about the uses of active, exploratory geometry carried out with interactive computer software.

Download or read book Spinoza s Geometry of Power written by Valtteri Viljanen and published by Cambridge University Press. This book was released on 2011-09-29 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This work examines the unique way in which Benedict de Spinoza (1632–77) combines two significant philosophical principles: that real existence requires causal power and that geometrical objects display exceptionally clearly how things have properties in virtue of their essences. Valtteri Viljanen argues that underlying Spinoza's psychology and ethics is a compelling metaphysical theory according to which each and every genuine thing is an entity of power endowed with an internal structure akin to that of geometrical objects. This allows Spinoza to offer a theory of existence and of action - human and non-human alike - as dynamic striving that takes place with the same kind of necessity and intelligibility that pertain to geometry. Viljanen's fresh and original study will interest a wide range of readers in Spinoza studies and early modern philosophy more generally.

Download or read book Shape written by Jordan Ellenberg and published by Penguin. This book was released on 2021-05-25 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: An instant New York Times Bestseller! “Unreasonably entertaining . . . reveals how geometric thinking can allow for everything from fairer American elections to better pandemic planning.” —The New York Times From the New York Times-bestselling author of How Not to Be Wrong—himself a world-class geometer—a far-ranging exploration of the power of geometry, which turns out to help us think better about practically everything. How should a democracy choose its representatives? How can you stop a pandemic from sweeping the world? How do computers learn to play Go, and why is learning Go so much easier for them than learning to read a sentence? Can ancient Greek proportions predict the stock market? (Sorry, no.) What should your kids learn in school if they really want to learn to think? All these are questions about geometry. For real. If you're like most people, geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel. Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: Where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. The word "geometry"comes from the Greek for "measuring the world." If anything, that's an undersell. Geometry doesn't just measure the world—it explains it. Shape shows us how.

Download or read book The Facts on File Geometry Handbook written by Catherine A. Gorini and published by Infobase Publishing. This book was released on 2014-05-14 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains a history of the subject of geometry, including more than 3,000 entries providing definitions and explanations of related topics, plus brief biographies of over 300 scientists.

Download or read book Geometry from a Differentiable Viewpoint written by John McCleary and published by Cambridge University Press. This book was released on 1994 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a new treatment of differential geometry which is designed to make the subject approachable for advanced undergraduates.

Download or read book Turtle Geometry written by Harold Abelson and published by MIT Press. This book was released on 1986-07-09 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: Turtle Geometry presents an innovative program of mathematical discovery that demonstrates how the effective use of personal computers can profoundly change the nature of a student's contact with mathematics. Using this book and a few simple computer programs, students can explore the properties of space by following an imaginary turtle across the screen. The concept of turtle geometry grew out of the Logo Group at MIT. Directed by Seymour Papert, author of Mindstorms, this group has done extensive work with preschool children, high school students and university undergraduates.

Download or read book Taking SketchUp Pro to the Next Level written by Aaron Dietzen aka 'The SketchUp Guy' and published by Packt Publishing Ltd. This book was released on 2022-09-28 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Create beautiful custom materials and leverage powerful extensions for efficient modeling Key FeaturesUnderstand how to get the most out of SketchUp's powerful native tools with key images printed in colorCustomize and transform your workspace for efficient 3D modelingGo beyond SketchUp's capabilities with extensions and free online resourcesBook Description Anyone who's worked with it will know that SketchUp is the quickest and easiest way to create 3D models. While its approachable interface makes it super easy to learn, this book will show you how the extremely capable SketchUp software can take you far beyond what you may have initially thought possible. Get ready to level up from a basic user to becoming a SketchUp ninja! Each chapter will take you through the capabilities of SketchUp, challenging you to use tools in innovative ways. This includes organizing your model, modifying native commands, customizing your interface, utilizing inferencing, and much more. Additionally, you'll learn about the extensions that can be added to SketchUp to supplement the tools you have been using, allowing you to make your 3D modeling process quicker, easier, and more powerful. By the end of this SketchUp book, you'll have an enhanced understanding of how to use the impressive range of tools and be on your way to customizing SketchUp for your one-of-a-kind workflow. What you will learnRecap the basics of navigation and SketchUp's native modeling toolsModify commands, toolbars, and shortcuts to improve your modeling efficiencyUse default templates, as well as create custom templatesOrganize your models with groups, components, tags, and scenesAnalyze your own modeling workflow and understand how to improve itDiscover extensions and online repositories that unlock the advanced capabilities of SketchUpLeverage your existing SketchUp Pro subscription for even better resultsWho this book is for This book is for designers, architects, and professional modelers who have used SketchUp before, perhaps self-taught, or have completed software training but find themselves needing more than just the basics from SketchUp. The book assumes that you have spent some time in SketchUp and have basic modeling experience.

Download or read book Molecular Geometry of Body Pattern in Birds written by Antonio Lima-de-Faria and published by Springer Science & Business Media. This book was released on 2012-03-19 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: After having read this book you will never see birds in the same way again. The unexpected patterns displayed by a bird’s body have been seen as bizarre events that demanded little attention or were described as ‘amazing curiosities’. None of these surprising features seem to be fortuitous. They appear to be an integral part of a rigid order and a coherent geometry, which is directed by simple gene interactions and molecular cascades occurring at various cellular levels, and at different times, during the organism’s development. A novel geometry unfolds in front of your eyes, giving the body configurations another meaning. Lima-de-Faria is Professor Emeritus of Molecular Cytogenetics at Lund University, Lund, Sweden. This is his sixth book dealing with the molecular organization of the chromosome and its implications for the understanding of the mechanisms responsible for biological evolution.

Download or read book Topology and Geometry in Dimension Three written by Weiping Li and published by American Mathematical Soc.. This book was released on 2011 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of a conference held from June 4-6, 2010, at Oklahoma State University, in honor of William (Bus) Jaco's 70th birthday. His contributions to research in low dimensional geometry and topology and to the American mathematical community, especially through his work for the American Mathematical Society, were recognized during the conference. The focus of the conference was on triangulations and geometric structures for three-dimensional manifolds. The papers in this volume present significant new results on these topics, as well as in geometric group theory.

Download or read book Rigidity in Dynamics and Geometry written by Marc Burger and published by Springer Science & Business Media. This book was released on 2002-05-13 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an offspring of the special semester "Ergodic Theory, Geometric Rigidity and Number Theory" held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK, from January until July, 2000. Some of the major recent developments in rigidity theory, geometric group theory, flows on homogeneous spaces and Teichmüller spaces, quasi-conformal geometry, negatively curved groups and spaces, Diophantine approximation, and bounded cohomology are presented here. The authors have given special consideration to making the papers accessible to graduate students, with most of the contributions starting at an introductory level and building up to presenting topics at the forefront in this active field of research. The volume contains surveys and original unpublished results as well, and is an invaluable source also for the experienced researcher.

Download or read book Differential Geometry And Physics Proceedings Of The 23th International Conference Of Differential Geometric Methods In Theoretical Physics written by Weiping Zhang and published by World Scientific. This book was released on 2006-12-11 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volumes provides a comprehensive review of interactions between differential geometry and theoretical physics, contributed by many leading scholars in these fields. The contributions promise to play an important role in promoting the developments in these exciting areas. Besides the plenary talks, the coverage includes: models and related topics in statistical physics; quantum fields, strings and M-theory; Yang-Mills fields, knot theory and related topics; K-theory, including index theory and non-commutative geometry; mirror symmetry, conformal and topological quantum field theory; development of integrable systems; and random matrix theory.

Download or read book Geometry of Single point Turning Tools and Drills written by Viktor P. Astakhov and published by Springer Science & Business Media. This book was released on 2010-07-29 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry of Single-Point Turning Tools and Drills outlines clear objectives of cutting tool geometry selection and optimization, using multiple examples to provide a thorough explanation. It addresses several urgent problems that many present-day tool manufacturers, tool application specialists, and tool users, are facing. It is both a practical guide, offering useful, practical suggestions for the solution of common problems, and a useful reference on the most important aspects of cutting tool design, application, and troubleshooting practices. Covering emerging trends in cutting tool design, cutting tool geometry, machining regimes, and optimization of machining operations, Geometry of Single-Point Turning Tools and Drills is an indispensable source of information for tool designers, manufacturing engineers, research workers, and students.

Download or read book Non Euclidean Laguerre Geometry and Incircular Nets written by Alexander I. Bobenko and published by Springer Nature. This book was released on 2021-10-29 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is a comprehensive and yet accessible introduction to non-Euclidean Laguerre geometry, for which there exists no previous systematic presentation in the literature. Moreover, we present new results by demonstrating all essential features of Laguerre geometry on the example of checkerboard incircular nets. Classical (Euclidean) Laguerre geometry studies oriented hyperplanes, oriented hyperspheres, and their oriented contact in Euclidean space. We describe how this can be generalized to arbitrary Cayley-Klein spaces, in particular hyperbolic and elliptic space, and study the corresponding groups of Laguerre transformations. We give an introduction to Lie geometry and describe how these Laguerre geometries can be obtained as subgeometries. As an application of two-dimensional Lie and Laguerre geometry we study the properties of checkerboard incircular nets.

Download or read book Handbook of Convex Geometry written by Bozzano G Luisa and published by Elsevier. This book was released on 2014-06-28 with total page 769 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Convex Geometry, Volume B offers a survey of convex geometry and its many ramifications and connections with other fields of mathematics, including convexity, lattices, crystallography, and convex functions. The selection first offers information on the geometry of numbers, lattice points, and packing and covering with convex sets. Discussions focus on packing in non-Euclidean spaces, problems in the Euclidean plane, general convex bodies, computational complexity of lattice point problem, centrally symmetric convex bodies, reduction theory, and lattices and the space of lattices. The text then examines finite packing and covering and tilings, including plane tilings, monohedral tilings, bin packing, and sausage problems. The manuscript takes a look at valuations and dissections, geometric crystallography, convexity and differential geometry, and convex functions. Topics include differentiability, inequalities, uniqueness theorems for convex hypersurfaces, mixed discriminants and mixed volumes, differential geometric characterization of convexity, reduction of quadratic forms, and finite groups of symmetry operations. The selection is a dependable source of data for mathematicians and researchers interested in convex geometry.

Download or read book The Wise Master Builder Platonic Geometry in Plans of Medieval Abbeys and Cathederals written by Nigel Hiscock and published by Routledge. This book was released on 2018-05-08 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title was first published in 2000: Did the plan of medieval churches have any underlying symbolic meaning? This work re-opens the debate about the importance of geometry and symbolism in medieval architectural design and argues the case for attributing an intellectual meaning to the planning of abbeys and cathedrals. In challenging prevailing claims for the use of arithmetical rations in architectural design, notably those based on the square root of two, Dr Hiscock advances a perspective consisting of proportions derived from the figures of Platonic geometry - the square, the equilateral triangle and the pentagon - and provides evidence for the symbolic interpretation of these figures. The investigation further reveals whole series of geometric relationships between some of England's most celebrated Norman cathedrals, such as Norwich or Durham, together with a wide sample from the Continent, from Old St Peter's in Rome to Chartres Cathedral, and sets out a comprehensive design method in each case. Hiscock first demonstrates the proposition that the ideas of Christian Platonism, including number and geometry, remained current and were employed in the thought of the early Middle Ages. In particular, he argues that they can be associated with the leading persons in the 10th-century revival of monasticism and that they found expression in the "white mantle of churches" that spread across Western Europe at the end of the first millennium AD. The book then provides a detailed analysis of the geometric proportions of church plans between the 9th and 12th centuries in Germany, France and in England. This research seeks to demonstrate that a coherent sequence of geometric forms can be seen in thse plans, forms which correspond to the key figures of Platonic geometry as understood in the context of Christian Platonist thought. In conclusion, the author shows how the system of design proposed could be set out on site using the known working methods of medieval masons.

Download or read book College Geometry written by David C. Kay and published by CRC Press. This book was released on 2011-06-24 with total page 655 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for mathematics majors and other students who intend to teach mathematics at the secondary school level, College Geometry: A Unified Development unifies the three classical geometries within an axiomatic framework. The author develops the axioms to include Euclidean, elliptic, and hyperbolic geometry, showing how geometry has real and far-reaching implications. He approaches every topic as a fresh, new concept and carefully defines and explains geometric principles. The book begins with elementary ideas about points, lines, and distance, gradually introducing more advanced concepts such as congruent triangles and geometric inequalities. At the core of the text, the author simultaneously develops the classical formulas for spherical and hyperbolic geometry within the axiomatic framework. He explains how the trigonometry of the right triangle, including the Pythagorean theorem, is developed for classical non-Euclidean geometries. Previously accessible only to advanced or graduate students, this material is presented at an elementary level. The book also explores other important concepts of modern geometry, including affine transformations and circular inversion. Through clear explanations and numerous examples and problems, this text shows step-by-step how fundamental geometric ideas are connected to advanced geometry. It represents the first step toward future study of Riemannian geometry, Einstein’s relativity, and theories of cosmology.

Download or read book From Groups to Geometry and Back written by Vaughn Climenhaga and published by American Mathematical Soc.. This book was released on 2017-04-07 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects. This book explores these connections between group theory and geometry, introducing some of the main ideas of transformation groups, algebraic topology, and geometric group theory. The first half of the book introduces basic notions of group theory and studies symmetry groups in various geometries, including Euclidean, projective, and hyperbolic. The classification of Euclidean isometries leads to results on regular polyhedra and polytopes; the study of symmetry groups using matrices leads to Lie groups and Lie algebras. The second half of the book explores ideas from algebraic topology and geometric group theory. The fundamental group appears as yet another group associated to a geometric object and turns out to be a symmetry group using covering spaces and deck transformations. In the other direction, Cayley graphs, planar models, and fundamental domains appear as geometric objects associated to groups. The final chapter discusses groups themselves as geometric objects, including a gentle introduction to Gromov's theorem on polynomial growth and Grigorchuk's example of intermediate growth. The book is accessible to undergraduate students (and anyone else) with a background in calculus, linear algebra, and basic real analysis, including topological notions of convergence and connectedness. This book is a result of the MASS course in algebra at Penn State University in the fall semester of 2009.