Configurations Of Points And Lines

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Configurations Of Points And Lines

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Author : Branko Grünbaum
language : en
Publisher: American Mathematical Soc.
Release Date : 2009

Configurations Of Points And Lines written by Branko Grünbaum and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

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

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Author : Branko Grünbaum
language : en
Publisher: American Mathematical Soc.
Release Date : 2009

Configurations Of Points And Lines written by Branko Grünbaum and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

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

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Author : Tomaz Pisanski
language : en
Publisher: Springer Science & Business Media
Release Date : 2013

Configurations From A Graphical Viewpoint written by Tomaz Pisanski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.

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.

Pencils Of Cubics And Algebraic Curves In The Real Projective Plane

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Author : Séverine Fiedler - Le Touzé
language : en
Publisher: CRC Press
Release Date : 2018-12-07

Pencils Of Cubics And Algebraic Curves In The Real Projective Plane written by Séverine Fiedler - Le Touzé and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-07 with Mathematics categories.

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
language : en
Publisher: American Mathematical Society
Release Date : 2024-07-25

The Mathematical Playground written by Alissa S. Crans and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-25 with Mathematics categories.

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 :
language : en
Publisher: Elsevier
Release Date : 2011-08-26

Combinatorial Mathematics Optimal Designs And Their Applications written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-26 with Mathematics categories.

Combinatorial Mathematics, Optimal Designs, and Their Applications

Riemann And Klein Surfaces Automorphisms Symmetries And Moduli Spaces

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Author : Milagros Izquierdo
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-11-21

Riemann And Klein Surfaces Automorphisms Symmetries And Moduli Spaces written by Milagros Izquierdo and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-21 with Mathematics categories.

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.

Forbidden Configurations In Discrete Geometry

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Author : David Eppstein
language : en
Publisher: Cambridge University Press
Release Date : 2018-05-17

Forbidden Configurations In Discrete Geometry written by David Eppstein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-17 with Computers categories.

Unifies discrete and computational geometry by using forbidden patterns of points to characterize many of its problems.

Rigidity And Symmetry

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Author : Robert Connelly
language : en
Publisher: Springer
Release Date : 2014-06-11

Rigidity And Symmetry written by Robert Connelly and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-11 with Mathematics categories.

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.

Encyclopaedia Of Mathematics Set

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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-02-28

Encyclopaedia Of Mathematics Set written by Michiel Hazewinkel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-02-28 with Mathematics categories.

The Encyclopaedia of Mathematics is the most up-to-date, authoritative and comprehensive English-language work of reference in mathematics which exists today. With over 7,000 articles from `A-integral' to `Zygmund Class of Functions', supplemented with a wealth of complementary information, and an index volume providing thorough cross-referencing of entries of related interest, the Encyclopaedia of Mathematics offers an immediate source of reference to mathematical definitions, concepts, explanations, surveys, examples, terminology and methods. The depth and breadth of content and the straightforward, careful presentation of the information, with the emphasis on accessibility, makes the Encyclopaedia of Mathematics an immensely useful tool for all mathematicians and other scientists who use, or are confronted by, mathematics in their work. The Enclyclopaedia of Mathematics provides, without doubt, a reference source of mathematical knowledge which is unsurpassed in value and usefulness. It can be highly recommended for use in libraries of universities, research institutes, colleges and even schools.