Configurations Of Points And Lines

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Configurations of Points and Lines

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Author : Branko Grünbaum
Publisher : American Mathematical Soc.
ISBN 13 : 0821843087
Total Pages : 421 pages
Book Rating : 4.8/5 (218 download)

Book Synopsis Configurations of Points and Lines by : Branko Grünbaum

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.

Forbidden Configurations in Discrete Geometry

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Author : David Eppstein
Publisher : Cambridge University Press
ISBN 13 : 1108423914
Total Pages : 241 pages
Book Rating : 4.1/5 (84 download)

Book Synopsis Forbidden Configurations in Discrete Geometry by : David Eppstein

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.

Lines and Curves

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Author : Victor Gutenmacher
Publisher : Springer Science & Business Media
ISBN 13 : 1475738099
Total Pages : 166 pages
Book Rating : 4.4/5 (757 download)

Book Synopsis Lines and Curves by : Victor Gutenmacher

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

Forbidden Configurations in Discrete Geometry

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Author : David Eppstein
Publisher : Cambridge University Press
ISBN 13 : 1108540279
Total Pages : 241 pages
Book Rating : 4.1/5 (85 download)

Book Synopsis Forbidden Configurations in Discrete Geometry by : David Eppstein

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: 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.

Rigidity and Symmetry

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Author : Robert Connelly
Publisher : Springer
ISBN 13 : 1493907816
Total Pages : 378 pages
Book Rating : 4.4/5 (939 download)

Book Synopsis Rigidity and Symmetry by : Robert Connelly

Download or read book Rigidity and Symmetry written by Robert Connelly and published by Springer. This book was released on 2014-06-11 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains recent contributions to the fields of rigidity and symmetry with two primary focuses: to present the mathematically rigorous treatment of rigidity of structures and to explore the interaction of geometry, algebra and combinatorics. Contributions present recent trends and advances in discrete geometry, particularly in the theory of polytopes. 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, classical geometry, hyperbolic geometry and topology. Overall, the book shows how researchers from diverse backgrounds explore connections among the various discrete structures with symmetry as the unifying theme. The volume will be a valuable source as an introduction to the ideas of both combinatorial and geometric rigidity theory and its applications, incorporating the surprising impact of symmetry. It will appeal to students at both the advanced undergraduate and graduate levels, as well as post docs, structural engineers and chemists.

Geometry of Lie Groups

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Author : B. Rosenfeld
Publisher : Springer Science & Business Media
ISBN 13 : 147575325X
Total Pages : 414 pages
Book Rating : 4.4/5 (757 download)

Book Synopsis Geometry of Lie Groups by : B. Rosenfeld

Download or read book Geometry of Lie Groups written by B. Rosenfeld and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the result of many years of research in Non-Euclidean Geometries and Geometry of Lie groups, as well as teaching at Moscow State University (1947- 1949), Azerbaijan State University (Baku) (1950-1955), Kolomna Pedagogical Col lege (1955-1970), Moscow Pedagogical University (1971-1990), and Pennsylvania State University (1990-1995). My first books on Non-Euclidean Geometries and Geometry of Lie groups were written in Russian and published in Moscow: Non-Euclidean Geometries (1955) [Ro1] , Multidimensional Spaces (1966) [Ro2] , and Non-Euclidean Spaces (1969) [Ro3]. In [Ro1] I considered non-Euclidean geometries in the broad sense, as geometry of simple Lie groups, since classical non-Euclidean geometries, hyperbolic and elliptic, are geometries of simple Lie groups of classes Bn and D , and geometries of complex n and quaternionic Hermitian elliptic and hyperbolic spaces are geometries of simple Lie groups of classes An and en. [Ro1] contains an exposition of the geometry of classical real non-Euclidean spaces and their interpretations as hyperspheres with identified antipodal points in Euclidean or pseudo-Euclidean spaces, and in projective and conformal spaces. Numerous interpretations of various spaces different from our usual space allow us, like stereoscopic vision, to see many traits of these spaces absent in the usual space.

Configurations from a Graphical Viewpoint

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Author : Tomaz Pisanski
Publisher : Springer Science & Business Media
ISBN 13 : 0817683631
Total Pages : 289 pages
Book Rating : 4.8/5 (176 download)

Book Synopsis Configurations from a Graphical Viewpoint by : Tomaz Pisanski

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.

$(16,6)$ Configurations and Geometry of Kummer Surfaces in ${\mathbb P}^3$

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Author : Maria del Rosario Gonzalez-Dorrego
Publisher : American Mathematical Soc.
ISBN 13 : 0821825747
Total Pages : 114 pages
Book Rating : 4.8/5 (218 download)

Book Synopsis $(16,6)$ Configurations and Geometry of Kummer Surfaces in ${\mathbb P}^3$ by : Maria del Rosario Gonzalez-Dorrego

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 114 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.

The Coxeter Legacy

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Author : Harold Scott Macdonald Coxeter
Publisher : American Mathematical Soc.
ISBN 13 : 9780821887608
Total Pages : 344 pages
Book Rating : 4.8/5 (876 download)

Book Synopsis The Coxeter Legacy by : Harold Scott Macdonald Coxeter

Download or read book The Coxeter Legacy written by Harold Scott Macdonald Coxeter and published by American Mathematical Soc.. This book was released on with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of essays on the legacy of mathematican Donald Coxeter is a mixture of surveys, updates, history, storytelling and personal memories covering both applied and abstract maths. Subjects include: polytopes, Coxeter groups, equivelar polyhedra, Ceva's theorum, and Coxeter and the artists.

Pencils of Cubics and Algebraic Curves in the Real Projective Plane

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Author : Séverine Fiedler - Le Touzé
Publisher : CRC Press
ISBN 13 : 0429838255
Total Pages : 257 pages
Book Rating : 4.4/5 (298 download)

Book Synopsis Pencils of Cubics and Algebraic Curves in the Real Projective Plane by : Séverine Fiedler - Le Touzé

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 257 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.

The Mathematical Playground

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Author : Alissa S. Crans
Publisher : American Mathematical Society
ISBN 13 : 1470477521
Total Pages : 382 pages
Book Rating : 4.4/5 (74 download)

Book Synopsis The Mathematical Playground by : Alissa S. Crans

Download or read book The Mathematical Playground written by Alissa S. Crans and published by American Mathematical Society. This book was released on 2024-07-25 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Welcome to The Mathematical Playground, a book celebrating more than thirty years of the problems column in the MAA undergraduate magazine, Math Horizons. Anecdotes, interviews, and historical sketches accompany the puzzles, conveying the vibrancy of the “Playground” community. The lively prose and humor used throughout the book reveal the enthusiasm and playfulness that have become the column's hallmark. Each chapter features a theme that helps illustrate community: from the Opening Acts—chronicling how interesting questions snowball into original research—to the Posers and Solvers themselves. These stories add an engaging dimension beyond the ample mathematical challenge. A particular highlight is a chapter introducing the seven editors who have produced “The Playground”, revealing the perspectives of the individuals behind the column. The Mathematical Playground has plenty to offer both novice and experienced solvers. The lighthearted, conversational style, together with copious hints, a problem-solving primer, and a detailed glossary, welcomes newcomers, regardless of their background, to the puzzle-solving world. The more seasoned solver will find over twenty new problems plus open-ended challenges and suggestions for further investigation. Whether you're a long-time Math Horizons reader, or encountering “The Playground” for the first time, you are invited into this celebration of the rich culture of recreational mathematics. Just remember the most important rule … Have fun!

Combinatorial Mathematics, Optimal Designs, and Their Applications

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Author :
Publisher : Elsevier
ISBN 13 : 0080867693
Total Pages : 401 pages
Book Rating : 4.0/5 (88 download)

Book Synopsis Combinatorial Mathematics, Optimal Designs, and Their Applications by :

Download or read book Combinatorial Mathematics, Optimal Designs, and Their Applications written by and published by Elsevier. This book was released on 2011-08-26 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial Mathematics, Optimal Designs, and Their Applications

Riemann and Klein Surfaces, Automorphisms, Symmetries and Moduli Spaces

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Author : Milagros Izquierdo
Publisher : American Mathematical Soc.
ISBN 13 : 1470410931
Total Pages : 362 pages
Book Rating : 4.4/5 (74 download)

Book Synopsis Riemann and Klein Surfaces, Automorphisms, Symmetries and Moduli Spaces by : Milagros Izquierdo

Download or read book Riemann and Klein Surfaces, Automorphisms, Symmetries and Moduli Spaces written by Milagros Izquierdo and published by American Mathematical Soc.. This book was released on 2014-11-21 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference on Riemann and Klein Surfaces, Symmetries and Moduli Spaces, in honor of Emilio Bujalance, held from June 24-28, 2013, at Linköping University. The conference and this volume are devoted to the mathematics that Emilio Bujalance has worked with in the following areas, all with a computational flavor: Riemann and Klein surfaces, automorphisms of real and complex surfaces, group actions on surfaces and topological properties of moduli spaces of complex curves and Abelian varieties.

Algorithms in Combinatorial Geometry

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Author : Herbert Edelsbrunner
Publisher : Springer Science & Business Media
ISBN 13 : 9783540137221
Total Pages : 446 pages
Book Rating : 4.1/5 (372 download)

Book Synopsis Algorithms in Combinatorial Geometry by : Herbert Edelsbrunner

Download or read book Algorithms in Combinatorial Geometry written by Herbert Edelsbrunner and published by Springer Science & Business Media. This book was released on 1987-07-31 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational geometry as an area of research in its own right emerged in the early seventies of this century. Right from the beginning, it was obvious that strong connections of various kinds exist to questions studied in the considerably older field of combinatorial geometry. For example, the combinatorial structure of a geometric problem usually decides which algorithmic method solves the problem most efficiently. Furthermore, the analysis of an algorithm often requires a great deal of combinatorial knowledge. As it turns out, however, the connection between the two research areas commonly referred to as computa tional geometry and combinatorial geometry is not as lop-sided as it appears. Indeed, the interest in computational issues in geometry gives a new and con structive direction to the combinatorial study of geometry. It is the intention of this book to demonstrate that computational and com binatorial investigations in geometry are doomed to profit from each other. To reach this goal, I designed this book to consist of three parts, acorn binatorial part, a computational part, and one that presents applications of the results of the first two parts. The choice of the topics covered in this book was guided by my attempt to describe the most fundamental algorithms in computational geometry that have an interesting combinatorial structure. In this early stage geometric transforms played an important role as they reveal connections between seemingly unrelated problems and thus help to structure the field.

Selected Papers of S. A. Amitsur with Commentary

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Author : Shimshon A. Amitsur
Publisher : American Mathematical Soc.
ISBN 13 : 9780821829240
Total Pages : 626 pages
Book Rating : 4.8/5 (292 download)

Book Synopsis Selected Papers of S. A. Amitsur with Commentary by : Shimshon A. Amitsur

Download or read book Selected Papers of S. A. Amitsur with Commentary written by Shimshon A. Amitsur and published by American Mathematical Soc.. This book was released on 2001 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handsomely-bound volume presents selected papers written by S.A. Amitsur on various topics in algebra. The approximately 50 papers in the first volume deal with general ring theory and rings satisfying a polynomial identity. A sampling of topics includes algebras over infinite fields, commutative linear differential operators, a generalization of Hilbert's Nullstellensatz, and central embeddings in semi-simple rings. Two essays on Amitsur's work and a biography also are included. The volume is not indexed. c. Book News Inc.

Handbook of Combinatorics Volume 1

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Author : Ronald L. Graham
Publisher : Elsevier
ISBN 13 : 9780444823465
Total Pages : 1124 pages
Book Rating : 4.8/5 (234 download)

Book Synopsis Handbook of Combinatorics Volume 1 by : Ronald L. Graham

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.

The Mathematical Gazette

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Author :
Publisher :
ISBN 13 :
Total Pages : 496 pages
Book Rating : 4.3/5 ( download)

Book Synopsis The Mathematical Gazette by :

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: