Configurations Of Points And Lines
Download Configurations Of Points And Lines PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Configurations Of Points And Lines book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
Configurations of Points and Lines
Author: Branko Grünbaum
language: en
Publisher: American Mathematical Soc.
Release Date: 2009
This is the only book on the topic of geometric configurations of points and lines. It presents in detail the history of the topic, with its surges and declines since its beginning in 1876. It covers all the advances in the field since the revival of interest in geometric configurations some 20 years ago. The author's contributions are central to this revival. In particular, he initiated the study of 4-configurations (that is, those that contain four points on each line, and four lines through each point); the results are fully described in the text. The main novelty in the approach to all geometric configurations is the concentration on their symmetries, which make it possible to deal with configurations of rather large sizes. The book brings the readers to the limits of present knowledge in a leisurely way, enabling them to enjoy the material as well as entice them to try their hand at expanding it.
Configurations of Points and Lines
Author: Branko Grünbaum
language: en
Publisher: American Mathematical Soc.
Release Date: 2009
This book discusses the topic of geometric configurations of points and lines. It presents in detail the history of the topic, with its surges and declines, since its beginning in 1876. It covers all advances in the field since the revival of interest in geometric configurations some 20 years ago.
Configurations from a Graphical Viewpoint
Author: Tomaz Pisanski
language: en
Publisher: Springer Science & Business Media
Release Date: 2013
Configurations can be studied from a graph-theoretical viewpoint via the so-called Levi graphs and lie at the heart of graphs, groups, surfaces, and geometries, all of which are very active areas of mathematical exploration. In this self-contained textbook, algebraic graph theory is used to introduce groups; topological graph theory is used to explore surfaces; and geometric graph theory is implemented to analyze incidence geometries. After a preview of configurations in Chapter 1, a concise introduction to graph theory is presented in Chapter 2, followed by a geometric introduction to groups in Chapter 3. Maps and surfaces are combinatorially treated in Chapter 4. Chapter 5 introduces the concept of incidence structure through vertex colored graphs, and the combinatorial aspects of classical configurations are studied. Geometric aspects, some historical remarks, references, and applications of classical configurations appear in the last chapter. With over two hundred illustrations, challenging exercises at the end of each chapter, a comprehensive bibliography, and a set of open problems, Configurations from a Graphical Viewpoint is well suited for a graduate graph theory course, an advanced undergraduate seminar, or a self-contained reference for mathematicians and researchers.