Geometry and its Applications in Arts, Nature and Technology

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Publisher : Springer Nature
ISBN 13 : 3030613984
Total Pages : 694 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Geometry and its Applications in Arts, Nature and Technology by : Georg Glaeser

Download or read book Geometry and its Applications in Arts, Nature and Technology written by Georg Glaeser and published by Springer Nature. This book was released on 2020-12-18 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book returns geometry to its natural habitats: the arts, nature and technology. Throughout the book, geometry comes alive as a tool to unlock the understanding of our world. Assuming only familiarity with high school mathematics, the book invites the reader to discover geometry through examples from biology, astronomy, architecture, design, photography, drawing, engineering and more. Lavishly illustrated with over 1200 figures, all of the geometric results are carefully derived from scratch, with topics from differential, projective and non-Euclidean geometry, as well as kinematics, introduced as the need arises. The mathematical results contained in the book range from very basic facts to recent results, and mathematical proofs are included although not necessary for comprehension. With its wide range of geometric applications, this self-contained volume demonstrates the ubiquity of geometry in our world, and may serve as a source of inspiration for architects, artists, designers, engineers, and natural scientists. This new edition has been completely revised and updated, with new topics and many new illustrations.

Geometry and Its Applications

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Publisher : Elsevier
ISBN 13 : 0080478034
Total Pages : 560 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Geometry and Its Applications by : Walter A. Meyer

Download or read book Geometry and Its Applications written by Walter A. Meyer and published by Elsevier. This book was released on 2006-02-21 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Meyer's Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry's usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers. - Realistic applications integrated throughout the text, including (but not limited to): - Symmetries of artistic patterns - Physics - Robotics - Computer vision - Computer graphics - Stability of architectural structures - Molecular biology - Medicine - Pattern recognition - Historical notes included in many chapters

Modern Geometry with Applications

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Publisher : Springer Science & Business Media
ISBN 13 : 1461208556
Total Pages : 193 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Modern Geometry with Applications by : George A. Jennings

Download or read book Modern Geometry with Applications written by George A. Jennings and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to modern geometry differs from other books in the field due to its emphasis on applications and its discussion of special relativity as a major example of a non-Euclidean geometry. Additionally, it covers the two important areas of non-Euclidean geometry, spherical geometry and projective geometry, as well as emphasising transformations, and conics and planetary orbits. Much emphasis is placed on applications throughout the book, which motivate the topics, and many additional applications are given in the exercises. It makes an excellent introduction for those who need to know how geometry is used in addition to its formal theory.

Differential Geometry and Its Applications

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Author :
Publisher : MAA
ISBN 13 : 9780883857489
Total Pages : 508 pages
Book Rating : 4.8/5 (574 download)

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Book Synopsis Differential Geometry and Its Applications by : John Oprea

Download or read book Differential Geometry and Its Applications written by John Oprea and published by MAA. This book was released on 2007-09-06 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the differential geometry of surfaces and its relevance to engineering and the sciences.

Tensors: Geometry and Applications

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Publisher : American Mathematical Soc.
ISBN 13 : 0821869078
Total Pages : 464 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Tensors: Geometry and Applications by : J. M. Landsberg

Download or read book Tensors: Geometry and Applications written by J. M. Landsberg and published by American Mathematical Soc.. This book was released on 2011-12-14 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensors are ubiquitous in the sciences. The geometry of tensors is both a powerful tool for extracting information from data sets, and a beautiful subject in its own right. This book has three intended uses: a classroom textbook, a reference work for researchers in the sciences, and an account of classical and modern results in (aspects of) the theory that will be of interest to researchers in geometry. For classroom use, there is a modern introduction to multilinear algebra and to the geometry and representation theory needed to study tensors, including a large number of exercises. For researchers in the sciences, there is information on tensors in table format for easy reference and a summary of the state of the art in elementary language. This is the first book containing many classical results regarding tensors. Particular applications treated in the book include the complexity of matrix multiplication, P versus NP, signal processing, phylogenetics, and algebraic statistics. For geometers, there is material on secant varieties, G-varieties, spaces with finitely many orbits and how these objects arise in applications, discussions of numerous open questions in geometry arising in applications, and expositions of advanced topics such as the proof of the Alexander-Hirschowitz theorem and of the Weyman-Kempf method for computing syzygies.

The Advanced Geometry of Plane Curves and Their Applications

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Publisher : Courier Corporation
ISBN 13 : 0486153436
Total Pages : 316 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis The Advanced Geometry of Plane Curves and Their Applications by : C. Zwikker

Download or read book The Advanced Geometry of Plane Curves and Their Applications written by C. Zwikker and published by Courier Corporation. This book was released on 2011-11-30 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Of chief interest to mathematicians, but physicists and others will be fascinated ... and intrigued by the fruitful use of non-Cartesian methods. Students ... should find the book stimulating." — British Journal of Applied Physics This study of many important curves, their geometrical properties, and their applications features material not customarily treated in texts on synthetic or analytic Euclidean geometry. Its wide coverage, which includes both algebraic and transcendental curves, extends to unusual properties of familiar curves along with the nature of lesser known curves. Informative discussions of the line, circle, parabola, ellipse, and hyperbola presuppose only the most elementary facts. The less common curves — cissoid, strophoid, spirals, the leminscate, cycloid, epicycloid, cardioid, and many others — receive introductions that explain both their basic and advanced properties. Derived curves-the involute, evolute, pedal curve, envelope, and orthogonal trajectories-are also examined, with definitions of their important applications. These range through the fields of optics, electric circuit design, hydraulics, hydrodynamics, classical mechanics, electromagnetism, crystallography, gear design, road engineering, orbits of subatomic particles, and similar areas in physics and engineering. The author represents the points of the curves by complex numbers, rather than the real Cartesian coordinates, an approach that permits simple, direct, and elegant proofs.

Spherical Geometry and Its Applications

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Publisher : CRC Press
ISBN 13 : 1000627527
Total Pages : 262 pages
Book Rating : 4.0/5 (6 download)

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Book Synopsis Spherical Geometry and Its Applications by : Marshall A. Whittlesey

Download or read book Spherical Geometry and Its Applications written by Marshall A. Whittlesey and published by CRC Press. This book was released on 2019-11-14 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spherical Geometry and Its Applications introduces spherical geometry and its practical applications in a mathematically rigorous form. The text can serve as a course in spherical geometry for mathematics majors. Readers from various academic backgrounds can comprehend various approaches to the subject. The book introduces an axiomatic system for spherical geometry and uses it to prove the main theorems of the subject. It also provides an alternate approach using quaternions. The author illustrates how a traditional axiomatic system for plane geometry can be modified to produce a different geometric world – but a geometric world that is no less real than the geometric world of the plane. Features: A well-rounded introduction to spherical geometry Provides several proofs of some theorems to appeal to larger audiences Presents principal applications: the study of the surface of the earth, the study of stars and planets in the sky, the study of three- and four-dimensional polyhedra, mappings of the sphere, and crystallography Many problems are based on propositions from the ancient text Sphaerica of Menelaus

Information Geometry and Its Applications

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Publisher : Springer
ISBN 13 : 4431559787
Total Pages : 378 pages
Book Rating : 4.4/5 (315 download)

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Book Synopsis Information Geometry and Its Applications by : Shun-ichi Amari

Download or read book Information Geometry and Its Applications written by Shun-ichi Amari and published by Springer. This book was released on 2016-02-02 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first comprehensive book on information geometry, written by the founder of the field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide range of applications, covering information science, engineering, and neuroscience. It consists of four parts, which on the whole can be read independently. A manifold with a divergence function is first introduced, leading directly to dualistic structure, the heart of information geometry. This part (Part I) can be apprehended without any knowledge of differential geometry. An intuitive explanation of modern differential geometry then follows in Part II, although the book is for the most part understandable without modern differential geometry. Information geometry of statistical inference, including time series analysis and semiparametric estimation (the Neyman–Scott problem), is demonstrated concisely in Part III. Applications addressed in Part IV include hot current topics in machine learning, signal processing, optimization, and neural networks. The book is interdisciplinary, connecting mathematics, information sciences, physics, and neurosciences, inviting readers to a new world of information and geometry. This book is highly recommended to graduate students and researchers who seek new mathematical methods and tools useful in their own fields.

Differential Geometry with Applications to Mechanics and Physics

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Publisher : CRC Press
ISBN 13 : 9780824703851
Total Pages : 480 pages
Book Rating : 4.7/5 (38 download)

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Book Synopsis Differential Geometry with Applications to Mechanics and Physics by : Yves Talpaert

Download or read book Differential Geometry with Applications to Mechanics and Physics written by Yves Talpaert and published by CRC Press. This book was released on 2000-09-12 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to differential geometry with applications to mechanics and physics. It covers topology and differential calculus in banach spaces; differentiable manifold and mapping submanifolds; tangent vector space; tangent bundle, vector field on manifold, Lie algebra structure, and one-parameter group of diffeomorphisms; exterior differential forms; Lie derivative and Lie algebra; n-form integration on n-manifold; Riemann geometry; and more. It includes 133 solved exercises.

Computational Geometry

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Publisher : Springer Science & Business Media
ISBN 13 : 3662042452
Total Pages : 370 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Computational Geometry by : Mark de Berg

Download or read book Computational Geometry written by Mark de Berg and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement.

Geometry with Applications and Proofs

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Publisher : Springer
ISBN 13 : 9462098603
Total Pages : 327 pages
Book Rating : 4.4/5 (62 download)

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Book Synopsis Geometry with Applications and Proofs by : Aad Goddijn

Download or read book Geometry with Applications and Proofs written by Aad Goddijn and published by Springer. This book was released on 2014-12-03 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows how geometry can be learned by starting with real world problems which are solved by intuition, common sense reasoning and experiments. Gradually the more formal demands of mathematical proofs get their proper place and make it possible to explore new applications. This process helps students to feel the need for precise definitions and procedures, to contribute to the construction of an axiomatic system, and to experience the power of systematic reasoning. The course is designed for students in a Nature & Technology strand which prepares for studying the sciences or technology at university level. Its goal was basically to reintroduce ‘proof’ in a meaningful way in the late 1990s Dutch secondary education curriculum. Following the educational view of the Freudenthal Institute this is not done by stating Euclid’s axioms on page one, but rather a starting point is chosen in students’ intuitions and tentative solutions of problems that are experienced as real and relevant. The photograph on the cover shows students exploring one of the problems from the midpart of the course in the computerlab.

An Introduction to Riemannian Geometry

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Publisher : Springer
ISBN 13 : 3319086669
Total Pages : 476 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis An Introduction to Riemannian Geometry by : Leonor Godinho

Download or read book An Introduction to Riemannian Geometry written by Leonor Godinho and published by Springer. This book was released on 2014-07-26 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity. The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semester courses in either of these subjects. The main ideas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making An Introduction to Riemannian Geometry ideal for self-study.

Geometric Methods and Applications

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Publisher : Springer Science & Business Media
ISBN 13 : 1461301378
Total Pages : 584 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Geometric Methods and Applications by : Jean Gallier

Download or read book Geometric Methods and Applications written by Jean Gallier and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: As an introduction to fundamental geometric concepts and tools needed for solving problems of a geometric nature using a computer, this book fills the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics, computer vision, or robotics that do not cover the underlying geometric concepts in detail. Gallier offers an introduction to affine, projective, computational, and Euclidean geometry, basics of differential geometry and Lie groups, and explores many of the practical applications of geometry. Some of these include computer vision, efficient communication, error correcting codes, cryptography, motion interpolation, and robot kinematics. This comprehensive text covers most of the geometric background needed for conducting research in computer graphics, geometric modeling, computer vision, and robotics and as such will be of interest to a wide audience including computer scientists, mathematicians, and engineers.

Emerging Applications of Algebraic Geometry

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Publisher : Springer Science & Business Media
ISBN 13 : 0387096868
Total Pages : 382 pages
Book Rating : 4.3/5 (87 download)

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Book Synopsis Emerging Applications of Algebraic Geometry by : Mihai Putinar

Download or read book Emerging Applications of Algebraic Geometry written by Mihai Putinar and published by Springer Science & Business Media. This book was released on 2008-12-10 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent advances in both the theory and implementation of computational algebraic geometry have led to new, striking applications to a variety of fields of research. The articles in this volume highlight a range of these applications and provide introductory material for topics covered in the IMA workshops on "Optimization and Control" and "Applications in Biology, Dynamics, and Statistics" held during the IMA year on Applications of Algebraic Geometry. The articles related to optimization and control focus on burgeoning use of semidefinite programming and moment matrix techniques in computational real algebraic geometry. The new direction towards a systematic study of non-commutative real algebraic geometry is well represented in the volume. Other articles provide an overview of the way computational algebra is useful for analysis of contingency tables, reconstruction of phylogenetic trees, and in systems biology. The contributions collected in this volume are accessible to non-experts, self-contained and informative; they quickly move towards cutting edge research in these areas, and provide a wealth of open problems for future research.

Stochastic Geometry and its Applications

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Publisher : Wiley
ISBN 13 : 9780470743645
Total Pages : 458 pages
Book Rating : 4.7/5 (436 download)

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Book Synopsis Stochastic Geometry and its Applications by : Dietrich Stoyan

Download or read book Stochastic Geometry and its Applications written by Dietrich Stoyan and published by Wiley. This book was released on 2009-03-16 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Wiley Paperback Series makes valuable content more accessible to a new generation of statisticians, mathematicians and scientists. Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The book deals with the following topics: point processes random sets random measures random shapes fibre and surface processes tessellations stereological methods. This book has served as the key reference in its field for over 20 years and is regarded as the best treatment of the subject of stochastic geometry, both as an subject with vital applications to spatial statistics and as a very interesting field of mathematics in its own right.

Geometry

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Publisher :
ISBN 13 : 9780321473318
Total Pages : 0 pages
Book Rating : 4.4/5 (733 download)

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Book Synopsis Geometry by : Alan Bass

Download or read book Geometry written by Alan Bass and published by . This book was released on 2007-04-17 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Geometry workbook makes the fundamental concepts of geometry accessible and interesting for college students and incorporates a variety of basic algebra skills in order to show the connection between Geometry and Algebra. Topics include: A Brief History of Geometry 1. Basic Geometry Concepts 2. More about Angles 3. Triangles 4. More about Triangles: Similarity and Congruence 5. Quadrilaterals 6. Polygons 7. Area and Perimeter 8. Circles 9. Volume and Surface Area 10. Basic Trigonometry

Projective Geometry and Its Applications to Computer Graphics

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Publisher : Prentice Hall
ISBN 13 :
Total Pages : 426 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Projective Geometry and Its Applications to Computer Graphics by : Michael A. Penna

Download or read book Projective Geometry and Its Applications to Computer Graphics written by Michael A. Penna and published by Prentice Hall. This book was released on 1986 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: