Shapes and Geometries

Shapes and Geometries PDF

Author: M. C. Delfour

Publisher: SIAM

Published: 2011-01-01

Total Pages: 637

ISBN-13: 0898719364

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Presents the latest groundbreaking theoretical foundation to shape optimization in a form accessible to mathematicians, scientists and engineers.

Shapes and Geometries

Shapes and Geometries PDF

Author: Michel C. Delfour

Publisher: SIAM

Published: 2001-01-01

Total Pages: 512

ISBN-13: 9780898714890

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The tools to use for problems where the modeling, optimization, or control variable is the structure of a geometric object.

Shape

Shape PDF

Author: Jordan Ellenberg

Publisher: Penguin

Published: 2021-05-25

Total Pages: 481

ISBN-13: 1984879065

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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.

Shapes and Geometries

Shapes and Geometries PDF

Author: M. C. Delfour

Publisher: SIAM

Published: 2011-01-01

Total Pages: 638

ISBN-13: 0898719828

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This considerably enriched new edition provides a self-contained presentation of the mathematical foundations, constructions, and tools necessary for studying problems where the modeling, optimization, or control variable is the shape or the structure of a geometric object.

The Changing Shape of Geometry

The Changing Shape of Geometry PDF

Author: Mathematical Association of America

Publisher: Cambridge University Press

Published: 2003-01-09

Total Pages: 572

ISBN-13: 9780521531627

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Collection of popular articles on geometry from distinguished mathematicians and educationalists.

The Shapes of Things

The Shapes of Things PDF

Author: Shawn W. Walker

Publisher: SIAM

Published: 2015-06-25

Total Pages: 156

ISBN-13: 1611973961

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Many things around us have properties that depend on their shape--for example, the drag characteristics of a rigid body in a flow. This self-contained overview of differential geometry explains how to differentiate a function (in the calculus sense) with respect to a "shape variable." This approach, which is useful for understanding mathematical models containing geometric partial differential equations (PDEs), allows readers to obtain formulas for geometric quantities (such as curvature) that are clearer than those usually offered in differential geometry texts. Readers will learn how to compute sensitivities with respect to geometry by developing basic calculus tools on surfaces and combining them with the calculus of variations. Several applications that utilize shape derivatives and many illustrations that help build intuition are included.

Euclid

Euclid PDF

Author: Shoo Rayner

Publisher:

Published: 2017-11-02

Total Pages: 54

ISBN-13: 9781908944368

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Geometry is brought to life as Euclid explains principles of Geometry to his friends. With jokes and lots of illustrations, discover the beauty of geometry and, before you know it, you too will soon be a friend of Euclid! Shoo Rayner adds humour and simplicity to a tricky subject. A perfect introduction.

Numerical Geometry of Non-Rigid Shapes

Numerical Geometry of Non-Rigid Shapes PDF

Author: Alexander M. Bronstein

Publisher: Springer Science & Business Media

Published: 2008-09-18

Total Pages: 346

ISBN-13: 0387733019

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Deformable objects are ubiquitous in the world surrounding us, on all levels from micro to macro. The need to study such shapes and model their behavior arises in a wide spectrum of applications, ranging from medicine to security. In recent years, non-rigid shapes have attracted growing interest, which has led to rapid development of the field, where state-of-the-art results from very different sciences - theoretical and numerical geometry, optimization, linear algebra, graph theory, machine learning and computer graphics, to mention several - are applied to find solutions. This book gives an overview of the current state of science in analysis and synthesis of non-rigid shapes. Everyday examples are used to explain concepts and to illustrate different techniques. The presentation unfolds systematically and numerous figures enrich the engaging exposition. Practice problems follow at the end of each chapter, with detailed solutions to selected problems in the appendix. A gallery of colored images enhances the text. This book will be of interest to graduate students, researchers and professionals in different fields of mathematics, computer science and engineering. It may be used for courses in computer vision, numerical geometry and geometric modeling and computer graphics or for self-study.

The Geometry of Multiple Images

The Geometry of Multiple Images PDF

Author: Olivier Faugeras

Publisher: MIT Press

Published: 2001

Total Pages: 682

ISBN-13: 9780262562041

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This book formalizes and analyzes the relations between multiple views of a scene from the perspective of various types of geometries. A key feature is that it considers Euclidean and affine geometries as special cases of projective geometry. Over the last forty years, researchers have made great strides in elucidating the laws of image formation, processing, and understanding by animals, humans, and machines. This book describes the state of knowledge in one subarea of vision, the geometric laws that relate different views of a scene. Geometry, one of the oldest branches of mathematics, is the natural language for describing three-dimensional shapes and spatial relations. Projective geometry, the geometry that best models image formation, provides a unified framework for thinking about many geometric problems are relevant to vision. The book formalizes and analyzes the relations between multiple views of a scene from the perspective of various types of geometries. A key feature is that it considers Euclidean and affine geometries as special cases of projective geometry. Images play a prominent role in computer communications. Producers and users of images, in particular three-dimensional images, require a framework for stating and solving problems. The book offers a number of conceptual tools and theoretical results useful for the design of machine vision algorithms. It also illustrates these tools and results with many examples of real applications.