Configurations Of Points And Lines

Author : Branko Grünbaum
Publisher : American Mathematical Soc.
ISBN 13 : 0821843087
Total Pages : 421 pages
Book Rating : 4.86/5 ( download)

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Download or read book Configurations of Points and Lines written by Branko Grünbaum and published by American Mathematical Soc.. This book was released on 2009 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Tomaz Pisanski
Publisher : Springer Science & Business Media
ISBN 13 : 0817683631
Total Pages : 289 pages
Book Rating : 4.34/5 ( download)

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Download or read book Configurations from a Graphical Viewpoint written by Tomaz Pisanski and published by Springer Science & Business Media. This book was released on 2013 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : David Eppstein
Publisher : Cambridge University Press
ISBN 13 : 1108423914
Total Pages : 241 pages
Book Rating : 4.15/5 ( download)

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Download or read book Forbidden Configurations in Discrete Geometry written by David Eppstein and published by Cambridge University Press. This book was released on 2018-05-17 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unifies discrete and computational geometry by using forbidden patterns of points to characterize many of its problems.

Author : David Eppstein
Publisher : Cambridge University Press
ISBN 13 : 1108542972
Total Pages : 242 pages
Book Rating : 4.75/5 ( download)

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Download or read book Forbidden Configurations in Discrete Geometry written by David Eppstein and published by Cambridge University Press. This book was released on 2018-05-17 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys the mathematical and computational properties of finite sets of points in the plane, covering recent breakthroughs on important problems in discrete geometry, and listing many open problems. It unifies these mathematical and computational views using forbidden configurations, which are patterns that cannot appear in sets with a given property, and explores the implications of this unified view. Written with minimal prerequisites and featuring plenty of figures, this engaging book will be of interest to undergraduate students and researchers in mathematics and computer science. Most topics are introduced with a related puzzle or brain-teaser. The topics range from abstract issues of collinearity, convexity, and general position to more applied areas including robust statistical estimation and network visualization, with connections to related areas of mathematics including number theory, graph theory, and the theory of permutation patterns. Pseudocode is included for many algorithms that compute properties of point sets.

Author : David Hilbert
Publisher : American Mathematical Soc.
ISBN 13 : 0821819984
Total Pages : 370 pages
Book Rating : 4.82/5 ( download)

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Download or read book Geometry and the Imagination written by David Hilbert and published by American Mathematical Soc.. This book was released on 1999 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This remarkable book endures as a true masterpiece of mathematical exposition. The book is overflowing with mathematical ideas, which are always explained clearly and elegantly, and above all, with penetrating insight. It is a joy to read, both for beginners and experienced mathematicians. Geometry and the Imagination is full of interesting facts, many of which you wish you had known before. The book begins with examples of the simplest curves and surfaces, including thread constructions of certain quadrics and other surfaces. The chapter on regular systems of points leads to the crystallographic groups and the regular polyhedra in $\mathbb{R}^3$. In this chapter, they also discuss plane lattices. By considering unit lattices, and throwing in a small amount of number theory when necessary, they effortlessly derive Leibniz's series: $\pi/4 = 1 - 1/3 + 1/5 - 1/7 + - \ldots$. In the section on lattices in three and more dimensions, the authors consider sphere-packing problems, including the famous Kepler problem. One of the most remarkable chapters is ``Projective Configurations''. In a short introductory section, Hilbert and Cohn-Vossen give perhaps the most concise and lucid description of why a general geometer would care about projective geometry and why such an ostensibly plain setup is truly rich in structure and ideas. The chapter on kinematics includes a nice discussion of linkages and the geometry of configurations of points and rods that are connected and, perhaps, constrained in some way. This topic in geometry has become increasingly important in recent times, especially in applications to robotics. This is another example of a simple situation that leads to a rich geometry. It would be hard to overestimate the continuing influence Hilbert-Cohn-Vossen's book has had on mathematicians of this century. It surely belongs in the pantheon of great mathematics books.

Author : Maria del Rosario Gonzalez-Dorrego
Publisher : American Mathematical Soc.
ISBN 13 : 0821825747
Total Pages : 101 pages
Book Rating : 4.47/5 ( download)

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Download or read book $(16,6)$ Configurations and Geometry of Kummer Surfaces in ${\mathbb P}^3$ written by Maria del Rosario Gonzalez-Dorrego and published by American Mathematical Soc.. This book was released on 1994 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: The philosophy of the first part of this work is to understand (and classify) Kummer surfaces by studying (16, 6) configurations. Chapter 1 is devoted to classifying (16, 6) configurations and studying their manifold symmetries and the underlying questions about finite subgroups of [italic capitals]PGL4([italic]k). In chapter 2 we use this information to give a complete classification of Kummer surfaces together with explicit equations and the explicit description of their singularities.

Author : Séverine Fiedler - Le Touzé
Publisher : CRC Press
ISBN 13 : 0429838255
Total Pages : 226 pages
Book Rating : 4.55/5 ( download)

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Download or read book Pencils of Cubics and Algebraic Curves in the Real Projective Plane written by Séverine Fiedler - Le Touzé and published by CRC Press. This book was released on 2018-12-07 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pencils of Cubics and Algebraic Curves in the Real Projective Plane thoroughly examines the combinatorial configurations of n generic points in RP2. Especially how it is the data describing the mutual position of each point with respect to lines and conics passing through others. The first section in this book answers questions such as, can one count the combinatorial configurations up to the action of the symmetric group? How are they pairwise connected via almost generic configurations? These questions are addressed using rational cubics and pencils of cubics for n = 6 and 7. The book’s second section deals with configurations of eight points in the convex position. Both the combinatorial configurations and combinatorial pencils are classified up to the action of the dihedral group D8. Finally, the third section contains plentiful applications and results around Hilbert’s sixteenth problem. The author meticulously wrote this book based upon years of research devoted to the topic. The book is particularly useful for researchers and graduate students interested in topology, algebraic geometry and combinatorics. Features: Examines how the shape of pencils depends on the corresponding configurations of points Includes topology of real algebraic curves Contains numerous applications and results around Hilbert’s sixteenth problem About the Author: Séverine Fiedler-le Touzé has published several papers on this topic and has been invited to present at many conferences. She holds a Ph.D. from University Rennes1 and was a post-doc at the Mathematical Sciences Research Institute in Berkeley, California.

Author : Ronald L. Graham
Publisher : Elsevier
ISBN 13 : 9780444823465
Total Pages : 1124 pages
Book Rating : 4.68/5 ( download)

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Download or read book Handbook of Combinatorics Volume 1 written by Ronald L. Graham and published by Elsevier. This book was released on 1995-12-11 with total page 1124 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Combinatorics, Volume 1 focuses on basic methods, paradigms, results, issues, and trends across the broad spectrum of combinatorics. The selection first elaborates on the basic graph theory, connectivity and network flows, and matchings and extensions. Discussions focus on stable sets and claw free graphs, nonbipartite matching, multicommodity flows and disjoint paths, minimum cost circulations and flows, special proof techniques for paths and circuits, and Hamilton paths and circuits in digraphs. The manuscript then examines coloring, stable sets, and perfect graphs and embeddings and minors. The book takes a look at random graphs, hypergraphs, partially ordered sets, and matroids. Topics include geometric lattices, structural properties, linear extensions and correlation, dimension and posets of bounded degree, hypergraphs and set systems, stability, transversals, and matchings, and phase transition. The manuscript also reviews the combinatorial number theory, point lattices, convex polytopes and related complexes, and extremal problems in combinatorial geometry. The selection is a valuable reference for researchers interested in combinatorics.

Author :
Publisher :
ISBN 13 :
Total Pages : 496 pages
Book Rating : 4.49/5 ( download)

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Download or read book The Mathematical Gazette written by and published by . This book was released on 1928 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Victor Gutenmacher
Publisher : Springer Science & Business Media
ISBN 13 : 1475738099
Total Pages : 166 pages
Book Rating : 4.94/5 ( download)

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Download or read book Lines and Curves written by Victor Gutenmacher and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: Broad appeal to undergraduate teachers, students, and engineers; Concise descriptions of properties of basic planar curves from different perspectives; useful handbook for software engineers; A special chapter---"Geometry on the Web"---will further enhance the usefulness of this book as an informal tutorial resource.; Good mathematical notation, descriptions of properties of lines and curves, and the illustration of geometric concepts facilitate the design of computer graphics tools and computer animation.; Video game designers, for example, will find a clear discussion and illustration of hard-to-understand trajectory design concepts.; Good supplementary text for geometry courses at the undergraduate and advanced high school levels