Geometry Illuminated
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Geometry Illuminated
Author: Matthew Harvey
language: en
Publisher: The Mathematical Association of America
Release Date: 2015-09-25
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.
Lobachevski Illuminated
Author: Seth Braver
language: en
Publisher: American Mathematical Soc.
Release Date: 2011-12-31
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.
Color Appearance Models
Author: Mark D. Fairchild
language: en
Publisher: John Wiley & Sons
Release Date: 2005-07-08
There is an ever-increasing demand for a standard way to transport colours among devices on the Internet, and for achieving colour fidelity across digital media. The rapid growth in colour imaging technology has led to the emergence of colour management systems. These systems require colour appearance models so that images produced in one medium and viewed in a particular environment, may be reproduced in a second medium and viewed under different conditions. The eagerly anticipated second edition of Colour Appearance Models brings the fundamental issues and current solutions in the area of colour appearance modelling together in a single place for those needing to solve practical problems or looking for background for ongoing research projects. This book provides the relevant information for an updated review of colour appearance and provide details of many of the most widely used models to date, for example, Nayatani et al., Hunt, and RLAB and the ATD and LLAB appearance models that are of increasing interest for some applications. It also includes the recently formulated CIECAM02 model that represents a significant improvement of CIECAM97S and is the best possible model based on current knowledge. Fairchild presents an updated overview of device-independent colour imaging and finally introduces the concept of image appearance modelling as a potential future direction for colour appearance modelling research. A website accompanies this text that lists developments, publications and calculations related to the material in this book.