Journal of Natural Geometry
Author:
Publisher:
Published: 2000
Total Pages: 342
ISBN-13:
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Geometry and its Applications in Arts, Nature and Technology
Author: Georg Glaeser
Publisher: Springer Nature
Published: 2020-12-18
Total Pages: 694
ISBN-13: 3030613984
DOWNLOAD EBOOKThis 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.
Natural Operations in Differential Geometry
Author: Ivan Kolar
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 440
ISBN-13: 3662029502
DOWNLOAD EBOOKThe aim of this work is threefold: First it should be a monographical work on natural bundles and natural op erators in differential geometry. This is a field which every differential geometer has met several times, but which is not treated in detail in one place. Let us explain a little, what we mean by naturality. Exterior derivative commutes with the pullback of differential forms. In the background of this statement are the following general concepts. The vector bundle A kT* M is in fact the value of a functor, which associates a bundle over M to each manifold M and a vector bundle homomorphism over f to each local diffeomorphism f between manifolds of the same dimension. This is a simple example of the concept of a natural bundle. The fact that exterior derivative d transforms sections of A kT* M into sections of A k+1T* M for every manifold M can be expressed by saying that d is an operator from A kT* M into A k+1T* M.
Sub-Riemannian Geometry
Author: Andre Bellaiche
Publisher: Birkhäuser
Published: 2012-12-06
Total Pages: 404
ISBN-13: 3034892101
DOWNLOAD EBOOKSub-Riemannian geometry (also known as Carnot geometry in France, and non-holonomic Riemannian geometry in Russia) has been a full research domain for fifteen years, with motivations and ramifications in several parts of pure and applied mathematics, namely: control theory classical mechanics Riemannian geometry (of which sub-Riemannian geometry constitutes a natural generalization, and where sub-Riemannian metrics may appear as limit cases) diffusion on manifolds analysis of hypoelliptic operators Cauchy-Riemann (or CR) geometry. Although links between these domains had been foreseen by many authors in the past, it is only in recent years that sub- Riemannian geometry has been recognized as a possible common framework for all these topics. This book provides an introduction to sub-Riemannian geometry and presents the state of the art and open problems in the field. It consists of five coherent and original articles by the leading specialists: Andr Bellache: The tangent space in sub-Riemannian geometry Mikhael Gromov: Carnot-Carathodory spaces seen from within Richard Montgomery: Survey of singular geodesics Hctor J. Sussmann: A cornucopia of four-dimensional abnormal sub-Riemannian minimizers Jean-Michel Coron: Stabilization of controllable systems.
The Fractal Geometry of Nature
Author: Benoit Mandelbrot
Publisher: Echo Point Books & Media, LLC
Published: 2021-07-16
Total Pages: 0
ISBN-13: 9781648370410
DOWNLOAD EBOOKWritten in a style that is accessible to a wide audience, The Fractal Geometry of Nature inspired popular interest in this emerging field. Mandelbrot's unique style, and rich illustrations will inspire readers of all backgrounds.
Perceiving Geometry
Author: Catherine Q. Howe
Publisher: Springer Science & Business Media
Published: 2005-08-16
Total Pages: 146
ISBN-13: 9780387254876
DOWNLOAD EBOOKDuring the last few centuries, natural philosophers, and more recently vision scientists, have recognized that a fundamental problem in biological vision is that the sources underlying visual stimuli are unknowable in any direct sense, because of the inherent ambiguity of the stimuli that impinge on sensory receptors. The light that reaches the eye from any scene conflates the contributions of reflectance, illumination, transmittance, and subsidiary factors that affect these primary physical parameters. Spatial properties such as the size, distance and orientation of physical objects are also conflated in light stimuli. As a result, the provenance of light reaching the eye at any moment is uncertain. This quandary is referred to as the inverse optics problem. This book considers the evidence that the human visual system solves this problem by incorporating past human experience of what retinal images have typically corresponded to in the real world.
Modern Geometric Structures and Fields
Author: Сергей Петрович Новиков
Publisher: American Mathematical Soc.
Published: 2006
Total Pages: 658
ISBN-13: 0821839292
DOWNLOAD EBOOKPresents the basics of Riemannian geometry in its modern form as geometry of differentiable manifolds and the important structures on them. This book shows that Riemannian geometry has a great influence to several fundamental areas of modern mathematics and its applications.
Lectures on Convex Geometry
Author: Daniel Hug
Publisher: Springer Nature
Published: 2020-08-27
Total Pages: 300
ISBN-13: 3030501809
DOWNLOAD EBOOKThis book provides a self-contained introduction to convex geometry in Euclidean space. After covering the basic concepts and results, it develops Brunn–Minkowski theory, with an exposition of mixed volumes, the Brunn–Minkowski inequality, and some of its consequences, including the isoperimetric inequality. Further central topics are then treated, such as surface area measures, projection functions, zonoids, and geometric valuations. Finally, an introduction to integral-geometric formulas in Euclidean space is provided. The numerous exercises and the supplementary material at the end of each section form an essential part of the book. Convexity is an elementary and natural concept. It plays a key role in many mathematical fields, including functional analysis, optimization, probability theory, and stochastic geometry. Paving the way to the more advanced and specialized literature, the material will be accessible to students in the third year and can be covered in one semester.
Information Geometry and Its Applications
Author: Shun-ichi Amari
Publisher: Springer
Published: 2016-02-02
Total Pages: 378
ISBN-13: 4431559787
DOWNLOAD EBOOKThis 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.
A New Approach to Differential Geometry using Clifford's Geometric Algebra
Author: John Snygg
Publisher: Springer Science & Business Media
Published: 2011-12-09
Total Pages: 472
ISBN-13: 081768283X
DOWNLOAD EBOOKDifferential geometry is the study of the curvature and calculus of curves and surfaces. A New Approach to Differential Geometry using Clifford's Geometric Algebra simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra. This presentation is relevant because Clifford algebra is an effective tool for dealing with the rotations intrinsic to the study of curved space. Complete with chapter-by-chapter exercises, an overview of general relativity, and brief biographies of historical figures, this comprehensive textbook presents a valuable introduction to differential geometry. It will serve as a useful resource for upper-level undergraduates, beginning-level graduate students, and researchers in the algebra and physics communities.
