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Author: Matthew Harvey Publisher: The Mathematical Association of America ISBN: 1939512115 Category : Mathematics Languages : en Pages : 561
Book Description
Geometry Illuminated is an introduction to geometry in the plane, both Euclidean and hyperbolic. It is designed to be used in an undergraduate course on geometry, and as such, its target audience is undergraduate math majors. However, much of it should be readable by anyone who is comfortable with the language of mathematical proof. Throughout, the goal is to develop the material patiently. One of the more appealing aspects of geometry is that it is a very "visual" subject. This book hopes to takes full advantage of that, with an extensive use of illustrations as guides. Geometry Illuminated is divided into four principal parts. Part 1 develops neutral geometry in the style of Hilbert, including a discussion of the construction of measure in that system, ultimately building up to the Saccheri-Legendre Theorem. Part 2 provides a glimpse of classical Euclidean geometry, with an emphasis on concurrence results, such as the nine-point circle. Part 3 studies transformations of the Euclidean plane, beginning with isometries and ending with inversion, with applications and a discussion of area in between. Part 4 is dedicated to the development of the Poincaré disk model, and the study of geometry within that model. While this material is traditional, Geometry Illuminated does bring together topics that are generally not found in a book at this level. Most notably, it explicitly computes parametric equations for the pseudosphere and its geodesics. It focuses less on the nature of axiomatic systems for geometry, but emphasizes rather the logical development of geometry within such a system. It also includes sections dealing with trilinear and barycentric coordinates, theorems that can be proved using inversion, and Euclidean and hyperbolic tilings.
Author: Matthew Harvey Publisher: The Mathematical Association of America ISBN: 1939512115 Category : Mathematics Languages : en Pages : 561
Book Description
Geometry Illuminated is an introduction to geometry in the plane, both Euclidean and hyperbolic. It is designed to be used in an undergraduate course on geometry, and as such, its target audience is undergraduate math majors. However, much of it should be readable by anyone who is comfortable with the language of mathematical proof. Throughout, the goal is to develop the material patiently. One of the more appealing aspects of geometry is that it is a very "visual" subject. This book hopes to takes full advantage of that, with an extensive use of illustrations as guides. Geometry Illuminated is divided into four principal parts. Part 1 develops neutral geometry in the style of Hilbert, including a discussion of the construction of measure in that system, ultimately building up to the Saccheri-Legendre Theorem. Part 2 provides a glimpse of classical Euclidean geometry, with an emphasis on concurrence results, such as the nine-point circle. Part 3 studies transformations of the Euclidean plane, beginning with isometries and ending with inversion, with applications and a discussion of area in between. Part 4 is dedicated to the development of the Poincaré disk model, and the study of geometry within that model. While this material is traditional, Geometry Illuminated does bring together topics that are generally not found in a book at this level. Most notably, it explicitly computes parametric equations for the pseudosphere and its geodesics. It focuses less on the nature of axiomatic systems for geometry, but emphasizes rather the logical development of geometry within such a system. It also includes sections dealing with trilinear and barycentric coordinates, theorems that can be proved using inversion, and Euclidean and hyperbolic tilings.
Author: Seth Braver Publisher: American Mathematical Soc. ISBN: 1470456400 Category : Education Languages : en Pages : 227
Book Description
Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2015! Lobachevski Illuminated provides an historical introduction to non-Euclidean geometry. Within its pages, readers will be guided step-by-step through a new translation of Lobachevski's groundbreaking book, The Theory of Parallels. Extensive commentary situates Lobachevski's work in its mathematical, historical, and philosophical context, thus granting readers a vision of the mysterious and beautiful world of non-Euclidean geometry as seen through the eyes of one of its discoverers. Although Lobachevski's 170-year-old text is challenging to read on its own, Seth Braver's carefully arranged “illuminations” render this classic accessible to any modern reader (student, professional, or layman) undaunted by high school mathematics.
Author: Jürgen Richter-Gebert Publisher: Springer Science & Business Media ISBN: 3642172865 Category : Mathematics Languages : en Pages : 573
Book Description
Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations.
Author: Ulf Leonhardt Publisher: Courier Corporation ISBN: 0486134903 Category : Science Languages : en Pages : 290
Book Description
Suitable for advanced undergraduate and graduate students of engineering, physics, and mathematics and scientific researchers of all types, this is the first authoritative text on invisibility and the science behind it. More than 100 full-color illustrations, plus exercises with solutions. 2010 edition.
Author: Ashis Kumar Samanta Publisher: BoD – Books on Demand ISBN: 1837691835 Category : Science Languages : en Pages : 240
Book Description
Advances in Colorimetry covers the fundamentals of the science of the measurement of color. It is organized into six sections: “Advanced Methods and Tools for Color Measuring and Matching”, “Fundamentals and Applications of Colorimetric Analysis”, “Applications of Colorimetric Analysis for Forensic and Defence Industry”, “Applications of Colorimetric Analysis for Food Industry”, “Applications of Colorimetric Analysis for Agriculture, Environmental, Medical and Pharmaceutical Industries”, and “Applications of Colorimetric Analysis for Textiles and Apparel Industry”. Chapters in these sections address colorimetric-related topics such as advances in colorimetric evaluation techniques for color measuring and matching, spectrophotometric color analysis, forensic analysis of bloodstain color, colorimetric characterization of natural dyes, and much more.
Author: Kurt Nassau Publisher: Elsevier ISBN: 0080529372 Category : Computers Languages : en Pages : 511
Book Description
The aim of this book is to assemble a series of chapters, written by experts in their fields, covering the basics of color - and then some more. In this way, readers are supplied with almost anything they want to know about color outside their own area of expertise. Thus, the color measurement expert, as well as the general reader, can find here information on the perception, causes, and uses of color. For the artist there are details on the causes, measurement, perception, and reproduction of color. Within each chapter, authors were requested to indicate directions of future efforts, where applicable. One might reasonably expect that all would have been learned about color in the more than three hundred years since Newton established the fundamentals of color science. This is not true because:• the measurement of color still has unresolved complexities (Chapter 2)• many of the fine details of color vision remain unknown (Chapter 3)• every few decades a new movement in art discovers original ways to use new pigments, and dyes continue to be discovered (Chapter 5)• the philosophical approach to color has not yet crystallized (Chapter 7)• new pigments and dyes continue to be discovered (Chapters 10 and 11)• the study of the biological and therapeutic effects of color is still in its infancy (Chapter 2).Color continues to develop towards maturity and the editor believes that there is much common ground between the sciences and the arts and that color is a major connecting bridge.
Author: Parisa Hariri Publisher: Springer Nature ISBN: 3030320685 Category : Mathematics Languages : en Pages : 504
Book Description
This book is an introduction to the theory of quasiconformal and quasiregular mappings in the euclidean n-dimensional space, (where n is greater than 2). There are many ways to develop this theory as the literature shows. The authors' approach is based on the use of metrics, in particular conformally invariant metrics, which will have a key role throughout the whole book. The intended readership consists of mathematicians from beginning graduate students to researchers. The prerequisite requirements are modest: only some familiarity with basic ideas of real and complex analysis is expected.
Author: Matthew Harvey
Author: Matthew Harvey
Author: Seth Braver
Author: Seth Braver
Author: Jürgen Richter-Gebert
Author: Ulf Leonhardt
Author: Benjamin Robert Haydon
Author: Ashis Kumar Samanta
Author: William C. Townsend
Author: Kurt Nassau
Author: Parisa Hariri