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Author: M. C. Delfour Publisher: SIAM ISBN: 0898719364 Category : Mathematics Languages : en Pages : 637
Book Description
Presents the latest groundbreaking theoretical foundation to shape optimization in a form accessible to mathematicians, scientists and engineers.
Author: M. C. Delfour Publisher: SIAM ISBN: 0898719364 Category : Mathematics Languages : en Pages : 637
Book Description
Presents the latest groundbreaking theoretical foundation to shape optimization in a form accessible to mathematicians, scientists and engineers.
Author: Jordan Ellenberg Publisher: Penguin ISBN: 1984879065 Category : Mathematics Languages : en Pages : 481
Book Description
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.
Author: Jordan Ellenberg Publisher: Penguin UK ISBN: 0241413532 Category : Mathematics Languages : en Pages : 354
Book Description
The international bestseller - a whip-smart, entertaining exploration of the geometry that underlies our world, from the author of How Not to Be Wrong How should a democracy choose its representatives? How can you stop a pandemic from sweeping the world? How do computers learn to play chess? 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? The answers to all these questions can be found in geometry. If you're like most people, geometry is a dimly-remembered exercise, handed down from the ancients, that you gladly left behind in school. It seemed to be a tortuous way of proving some fact about triangles that was obvious to you in the first place. That's not geometry. OK, it is geometry, but only a tiny part, that has as much to do with the modern, fast-moving discipline as conjugating a verb has to do with a great novel. In Shape, Sunday Times-bestselling author Jordan Ellenberg reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face, from the spread of coronavirus to rise of machine learning. The word 'geometry,' from the Greek, means 'measuring the world.' But geometry doesn't just measure the world - it explains it. Shape shows us how.
Author: Olivier Faugeras Publisher: MIT Press ISBN: 9780262562041 Category : Computers Languages : en Pages : 682
Book Description
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.
Author: M. C. Delfour Publisher: SIAM ISBN: 0898719828 Category : Mathematics Languages : en Pages : 638
Book Description
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.
Author: Shawn W. Walker Publisher: SIAM ISBN: 1611973961 Category : Mathematics Languages : en Pages : 152
Book Description
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.
Author: Alison Rodger Publisher: Butterworth-Heinemann ISBN: 1483106039 Category : Science Languages : en Pages : 202
Book Description
Molecular Geometry discusses topics relevant to the arrangement of atoms. The book is comprised of seven chapters that tackle several areas of molecular geometry. Chapter 1 reviews the definition and determination of molecular geometry, while Chapter 2 discusses the unified view of stereochemistry and stereochemical changes. Chapter 3 covers the geometry of molecules of second row atoms, and Chapter 4 deals with the main group elements beyond the second row. The book also talks about the complexes of transition metals and f-block elements, and then covers the organometallic compounds and transition metal clusters. The last chapter tackles the consequences of small, local variations in geometry. The text will be of great use to chemists who primarily deal with the properties of molecules and atoms.
Author: Alexander M. Bronstein Publisher: Springer Science & Business Media ISBN: 0387733019 Category : Computers Languages : en Pages : 346
Book Description
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.
Author: M. C. Delfour
Author: M. C. Delfour
Author: Jordan Ellenberg
Author: Michel C. Delfour
Author: Jordan Ellenberg
Author: Olivier Faugeras
Author: M. C. Delfour
Author: Chris Pritchard
Author: Shawn W. Walker
Author: Alison Rodger
Author: Alexander M. Bronstein