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Author: Matthew Harvey
Publisher: The Mathematical Association of America
ISBN: 1939512115
Category : Mathematics
Languages : en
Pages : 561
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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
Get Book Here
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 Steven Harvey
Publisher:
ISBN: 9781614446187
Category :
Languages : en
Pages : 543
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Book Description
Author:
Publisher: Lulu.com
ISBN: 1565430611
Category :
Languages : en
Pages : 42
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Book Description
Author: Seth Braver
Publisher: MAA
ISBN: 0883859793
Category : Mathematics
Languages : en
Pages : 250
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Book Description
A historical introduction to non-Euclidean geometry.
Author: Jürgen Richter-Gebert
Publisher: Springer Science & Business Media
ISBN: 3642172865
Category : Mathematics
Languages : en
Pages : 573
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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
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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: Marcus Fraser
Publisher: Gower Publishing Company, Limited
ISBN:
Category : Art
Languages : en
Pages : 48
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Book Description
This book is devoted to a monumental and superbly illuminated very large early fourteenth-century Mamluk Qur'an in muhaqqaq script. It constitutes the final part (Juz' 30) of a superb two-volume Qur'an of which the first volume is preserved in the National Museum in Damascus while the second volume, from which the present section originates, is widely dispersed. Remarkably, here the final part of the Qur'an is reunited with its magnificent and richly decorated double finispieces, thus reassembling what must have been among the most striking and lavishly illuminated sections of the entire manuscript. The high degree of inventiveness along with the overall quality of the manuscript point to the work of a master artist. Especially the geometric proficiency suggests the work of Muhammad ibn Mubadir, one of the leading illuminators in Mamluk Cairo at the turn of the thirteenth century. Although little is known of the life of this artist, his illumination in the Baybars al-Jashnagir Qur'an, now in the British Library, and a Qur'an copied in 1306-10 for an unknown patron, now in the Chester Beatty Library, constitute some of the most celebrated achievements of Mamluk Qur'an illumination.
Author: Roy S. Berns
Publisher: John Wiley & Sons
ISBN: 1119366682
Category : Science
Languages : en
Pages : 697
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Book Description
This book offers detailed coverage of color, colorants, the coloring of materials, and reproducing the color of materials through imaging. It combines the clarity and ease of earlier editions with significant updates about the advancement in color theory and technology. Provides guidance for how to use color measurement instrumentation, make a visual assessment, set a visual tolerance, and select a formulation Supplements material with numerical examples, graphs, and illustrations that clarify and explain complex subjects Expands coverage of topics including spatial vision, solid-state lighting, cameras and spectrophotometers, and translucent materials
Author: Parisa Hariri
Publisher: Springer Nature
ISBN: 3030320685
Category : Mathematics
Languages : en
Pages : 504
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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: Boris I. Sturman
Publisher: CRC Press
ISBN: 9782881244988
Category : Science
Languages : en
Pages : 252
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Book Description
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
