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Articles about the uses of active, exploratory geometry carried out with interactive computer software.
Richly detailed survey of the evolution of geometrical ideas and development of concepts of modern geometry: projective, Euclidean, and non-Euclidean geometry; role of geometry in Newtonian physics, calculus, relativity. Over 100 exercises with answers. 1966 edition.
Get the Knowledge Without the College! You are a writer. You dream of sharing your words with the world, and you're willing to put in the hard work to achieve success. You may have even considered earning your MFA, but for whatever reason--tuition costs, the time commitment, or other responsibilities--you've never been able to do it. Or maybe you've been looking for a self-guided approach so you don't have to go back to school. This book is for you. DIY MFA is the do-it-yourself alternative to a Master of Fine Arts in creative writing. By combining the three main components of a traditional MFA--writing, reading, and community--it teaches you how to craft compelling stories, engage your readers, and publish your work. Inside you'll learn how to: • Set customized goals for writing and learning. • Generate ideas on demand. • Outline your book from beginning to end. • Breathe life into your characters. • Master point of view, voice, dialogue, and more. • Read with a "writer's eye" to emulate the techniques of others. • Network like a pro, get the most out of writing workshops, and submit your work successfully. Writing belongs to everyone--not only those who earn a degree. With DIY MFA, you can take charge of your writing, produce high-quality work, get published, and build a writing career.
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.
Ever since the introduction by Rao in 1945 of the Fisher information metric on a family of probability distributions, there has been interest among statisticians in the application of differential geometry to statistics. This interest has increased rapidly in the last couple of decades with the work of a large number of researchers. Until now an impediment to the spread of these ideas into the wider community of statisticians has been the lack of a suitable text introducing the modern coordinate free approach to differential geometry in a manner accessible to statisticians. Differential Geometry and Statistics aims to fill this gap. The authors bring to this book extensive research experience in differential geometry and its application to statistics. The book commences with the study of the simplest differentiable manifolds - affine spaces and their relevance to exponential families, and goes on to the general theory, the Fisher information metric, the Amari connections and asymptotics. It culminates in the theory of vector bundles, principal bundles and jets and their applications to the theory of strings - a topic presently at the cutting edge of research in statistics and differential geometry.
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.
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.
This book offers a new treatment of differential geometry which is designed to make the subject approachable for advanced undergraduates.
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.
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.