Geometry Illuminated

Geometry Illuminated
Author: Matthew Harvey
Publisher: The Mathematical Association of America
Total Pages: 561
Release: 2015-09-25
Genre: Mathematics
ISBN: 1939512115

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

Lobachevski Illuminated
Author: Seth Braver
Publisher: MAA
Total Pages: 250
Release: 2011
Genre: Mathematics
ISBN: 0883859793

A historical introduction to non-Euclidean geometry.

Conformally Invariant Metrics and Quasiconformal Mappings

Conformally Invariant Metrics and Quasiconformal Mappings
Author: Parisa Hariri
Publisher: Springer Nature
Total Pages: 504
Release: 2020-04-11
Genre: Mathematics
ISBN: 3030320685

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.

Photovoltaic and Photo-refractive Effects in Noncentrosymmetric Materials

Photovoltaic and Photo-refractive Effects in Noncentrosymmetric Materials
Author: Boris I. Sturman
Publisher: CRC Press
Total Pages: 252
Release: 1992-05-28
Genre: Science
ISBN: 9782881244988

A technical treatment of the photovoltaic effect, one of the causes of photorefraction, which itself is used in holography, beam amplification and correction, wavefront reversals, and other fields. Focuses on the effect in ferro- and piezoelectric crystals. Translated from the Russian. Annotation copyrighted by Book News, Inc., Portland, OR

Handbook of Computational Geometry

Handbook of Computational Geometry
Author: J.R. Sack
Publisher: Elsevier
Total Pages: 1087
Release: 1999-12-13
Genre: Mathematics
ISBN: 0080529682

Computational Geometry is an area that provides solutions to geometric problems which arise in applications including Geographic Information Systems, Robotics and Computer Graphics. This Handbook provides an overview of key concepts and results in Computational Geometry. It may serve as a reference and study guide to the field. Not only the most advanced methods or solutions are described, but also many alternate ways of looking at problems and how to solve them.

Color Appearance Models

Color Appearance Models
Author: Mark D. Fairchild
Publisher: John Wiley & Sons
Total Pages: 485
Release: 2013-06-07
Genre: Technology & Engineering
ISBN: 1118653106

The essential resource for readers needing to understand visual perception and for those trying to produce, reproduce and measure color appearance in various applications such as imaging, entertainment, materials, design, architecture and lighting. This book builds upon the success of previous editions, and will continue to serve the needs of those professionals working in the field to solve practical problems or looking for background for on-going research projects. It would also act as a good course text for senior undergraduates and postgraduates studying color science. The 3rd Edition of Color Appearance Models contains numerous new and expanded sections providing an updated review of color appearance and includes many of the most widely used models to date, ensuring its continued success as the comprehensive resource on color appearance models. Key features: Presents the fundamental concepts and phenomena of color appearance (what objects look like in typical viewing situations) and practical techniques to measure, model and predict those appearances. Includes the clear explanation of fundamental concepts that makes the implementation of mathematical models very easy to understand. Explains many different types of models, and offers a clear context for the models, their use, and future directions in the field.

Discrete Geometry and Symmetry

Discrete Geometry and Symmetry
Author: Marston D. E. Conder
Publisher: Springer
Total Pages: 349
Release: 2018-06-11
Genre: Mathematics
ISBN: 331978434X

This book consists of contributions from experts, presenting a fruitful interplay between different approaches to discrete geometry. Most of the chapters were collected at the conference “Geometry and Symmetry” in Veszprém, Hungary from 29 June to 3 July 2015. The conference was dedicated to Károly Bezdek and Egon Schulte on the occasion of their 60th birthdays, acknowledging their highly regarded contributions in these fields. While the classical problems of discrete geometry have a strong connection to geometric analysis, coding theory, symmetry groups, and number theory, their connection to combinatorics and optimization has become of particular importance. The last decades have seen a revival of interest in discrete geometric structures and their symmetry. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry, group theory and geometry, combinatorial group theory, and hyperbolic geometry and topology. This book contains papers on new developments in these areas, including convex and abstract polytopes and their recent generalizations, tiling and packing, zonotopes, isoperimetric inequalities, and on the geometric and combinatorial aspects of linear optimization. The book is a valuable resource for researchers, both junior and senior, in the field of discrete geometry, combinatorics, or discrete optimization. Graduate students find state-of-the-art surveys and an open problem collection.

Handbook of Biological Confocal Microscopy

Handbook of Biological Confocal Microscopy
Author: James Pawley
Publisher: Springer Science & Business Media
Total Pages: 1018
Release: 2006-06-02
Genre: Science
ISBN: 9780387259215

Once the second edition was safely off to the printer, the 110 larger world of micro-CT and micro-MRI and the smaller world authors breathed a sigh of relief and relaxed, secure in the belief revealed by the scanning and transmission electron microscopes. that they would “never have to do that again. ” That lasted for 10 To round out the story we even have a chapter on what PowerPoint years. When we ?nally awoke, it seemed that a lot had happened. does to the results, and the annotated bibliography has been In particular, people were trying to use the Handbook as a text- updated and extended. book even though it lacked the practical chapters needed. There As with the previous editions, the editor enjoyed a tremendous had been tremendous progress in lasers and ?ber-optics and in our amount of good will and cooperation from the 124 authors understanding of the mechanisms underlying photobleaching and involved. Both I, and the light microscopy community in general, phototoxicity. It was time for a new book. I contacted “the usual owe them all a great debt of gratitude. On a more personal note, I suspects” and almost all agreed as long as the deadline was still a would like to thank Kathy Lyons and her associates at Springer for year away.

Lobachevski Illuminated

Lobachevski Illuminated
Author: Seth Braver
Publisher: American Mathematical Soc.
Total Pages: 227
Release: 2011-12-31
Genre: Education
ISBN: 1470456400

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.

Highly Resolved Synthetic Aperture Radar with Beam Steering

Highly Resolved Synthetic Aperture Radar with Beam Steering
Author: Ossowska, Alicja
Publisher: KIT Scientific Publishing
Total Pages: 256
Release: 2015-02-12
Genre: Technology (General)
ISBN: 3731503158

The present work deals with a highly resolved radar with a synthetic aperture (synthetic aperture radar - SAR), which uses a beam steering to improve performance. The first part of this work deals with the influence of various effects occurring in the hardware of the High-Resolution Wide-Swath SAR (HRWS SAR) system. A special focus was set to single bit quantization in multi-channel receiver. The second part of this work describes SAR processors for Sliding Spotlight mode.