Poncelet Porisms And Beyond

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Poncelet Porisms and Beyond

Author : Vladimir Dragović
Publisher : Springer Science & Business Media
ISBN 13 : 3034800150
Total Pages : 293 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Poncelet Porisms and Beyond by : Vladimir Dragović

Download or read book Poncelet Porisms and Beyond written by Vladimir Dragović and published by Springer Science & Business Media. This book was released on 2011-05-02 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the book is to present, in a complete and comprehensive way, areas of current research interlacing around the Poncelet porism: dynamics of integrable billiards, algebraic geometry of hyperelliptic Jacobians, and classical projective geometry of pencils of quadrics. The most important results and ideas, classical as well as modern, connected to the Poncelet theorem are presented, together with a historical overview analyzing the classical ideas and their natural generalizations. Special attention is paid to the realization of the Griffiths and Harris programme about Poncelet-type problems and addition theorems. This programme, formulated three decades ago, is aimed to understanding the higher-dimensional analogues of Poncelet problems and the realization of the synthetic approach of higher genus addition theorems.

Finding Ellipses: What Blaschke Products, Poncelet’s Theorem, and the Numerical Range Know about Each Other

Author : Ulrich Daepp
Publisher : American Mathematical Soc.
ISBN 13 : 147044383X
Total Pages : 268 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Finding Ellipses: What Blaschke Products, Poncelet’s Theorem, and the Numerical Range Know about Each Other by : Ulrich Daepp

Download or read book Finding Ellipses: What Blaschke Products, Poncelet’s Theorem, and the Numerical Range Know about Each Other written by Ulrich Daepp and published by American Mathematical Soc.. This book was released on 2018 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematicians delight in finding surprising connections between seemingly disparate areas of mathematics. Whole domains of modern mathematics have arisen from exploration of such connections--consider analytic number theory or algebraic topology. Finding Ellipses is a delight-filled romp across a three-way unexpected connection between complex analysis, linear algebra, and projective geometry. The book begins with Blaschke products, complex-analytic functions that are generalizations of disk automorphisms. In the analysis of Blaschke products, we encounter, in a quite natural way, an ellipse inside the unit disk. The story continues by introducing the reader to Poncelet's theorem--a beautiful result in projective geometry that ties together two conics and, in particular, two ellipses, one circumscribed by a polygon that is inscribed in the second. The Blaschke ellipse and the Poncelet ellipse turn out to be the same ellipse, and the connection is illuminated by considering the numerical range of a $2 \times 2$ matrix. The numerical range is a convex subset of the complex plane that contains information about the geometry of the transformation represented by a matrix. Through the numerical range of $n \times n$ matrices, we learn more about the interplay between Poncelet's theorem and Blaschke products. The story ranges widely over analysis, algebra, and geometry, and the exposition of the deep and surprising connections is lucid and compelling. Written for advanced undergraduates or beginning graduate students, this book would be the perfect vehicle for an invigorating and enlightening capstone exploration. The exercises and collection of extensive projects could be used as an embarkation point for a satisfying and rich research project. You are invited to read actively using the accompanying interactive website, which allows you to visualize the concepts in the book, experiment, and develop original conjectures.

Integrable Systems and Algebraic Geometry

Author : Ron Donagi
Publisher : Cambridge University Press
ISBN 13 : 1108715745
Total Pages : 421 pages
Book Rating : 4.1/5 (87 download)

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Book Synopsis Integrable Systems and Algebraic Geometry by : Ron Donagi

Download or read book Integrable Systems and Algebraic Geometry written by Ron Donagi and published by Cambridge University Press. This book was released on 2020-04-02 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.

Integrable Systems and Algebraic Geometry: Volume 1

Author : Ron Donagi
Publisher : Cambridge University Press
ISBN 13 : 110880358X
Total Pages : 421 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis Integrable Systems and Algebraic Geometry: Volume 1 by : Ron Donagi

Download or read book Integrable Systems and Algebraic Geometry: Volume 1 written by Ron Donagi and published by Cambridge University Press. This book was released on 2020-04-02 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: Created as a celebration of mathematical pioneer Emma Previato, this comprehensive book highlights the connections between algebraic geometry and integrable systems, differential equations, mathematical physics, and many other areas. The authors, many of whom have been at the forefront of research into these topics for the last decades, have all been influenced by Previato's research, as her collaborators, students, or colleagues. The diverse articles in the book demonstrate the wide scope of Previato's work and the inclusion of several survey and introductory articles makes the text accessible to graduate students and non-experts, as well as researchers. This first volume covers a wide range of areas related to integrable systems, often emphasizing the deep connections with algebraic geometry. Common themes include theta functions and Abelian varieties, Lax equations, integrable hierarchies, Hamiltonian flows and difference operators. These powerful tools are applied to spinning top, Hitchin, Painleve and many other notable special equations.

Asymptotic, Algebraic and Geometric Aspects of Integrable Systems

Author : Frank Nijhoff
Publisher : Springer Nature
ISBN 13 : 3030570002
Total Pages : 240 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Asymptotic, Algebraic and Geometric Aspects of Integrable Systems by : Frank Nijhoff

Download or read book Asymptotic, Algebraic and Geometric Aspects of Integrable Systems written by Frank Nijhoff and published by Springer Nature. This book was released on 2020-10-23 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume gathers together selected works from the 2018 “Asymptotic, Algebraic and Geometric Aspects of Integrable Systems” workshop that was held at TSIMF Yau Mathematical Sciences Center in Sanya, China, honoring Nalini Joshi on her 60th birthday. The papers cover recent advances in asymptotic, algebraic and geometric methods in the study of discrete integrable systems. The workshop brought together experts from fields such as asymptotic analysis, representation theory and geometry, creating a platform to exchange current methods, results and novel ideas. This volume's articles reflect these exchanges and can be of special interest to a diverse group of researchers and graduate students interested in learning about current results, new approaches and trends in mathematical physics, in particular those relevant to discrete integrable systems.

ICGG 2022 - Proceedings of the 20th International Conference on Geometry and Graphics

Author : Liang-Yee Cheng
Publisher : Springer Nature
ISBN 13 : 3031135881
Total Pages : 1080 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis ICGG 2022 - Proceedings of the 20th International Conference on Geometry and Graphics by : Liang-Yee Cheng

Download or read book ICGG 2022 - Proceedings of the 20th International Conference on Geometry and Graphics written by Liang-Yee Cheng and published by Springer Nature. This book was released on 2022-08-12 with total page 1080 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers recent achievements on the ever-expanding field of Geometry and Graphics on both analogical and digital fronts, from theoretical investigations to a broad range of applications, new teaching methodologies, and historical aspects. It is from 20th International Conference on Geometry and Graphics (ICGG2022), a series of conference that started in 1978 and promoted by International Society for Geometry and Graphics, which aims to foster international collaboration and stimulate the scientific research and teaching innovations in the multidisciplinary field. The contents of the book are organized in: Theoretical Geometry and Graphics; Applied Geometry and Graphics; Engineering Computer Graphics; Graphics Education; Geometry and Graphics in History, and are intent for the academics, researchers, and professionals in architecture, engineering, industrial design, mathematics, and arts.

The Universe of Conics

Author : Georg Glaeser
Publisher : Springer
ISBN 13 : 3662454505
Total Pages : 488 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis The Universe of Conics by : Georg Glaeser

Download or read book The Universe of Conics written by Georg Glaeser and published by Springer. This book was released on 2016-03-22 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents the classical theory of conics in a modern form. It includes many novel results that are not easily accessible elsewhere. The approach combines synthetic and analytic methods to derive projective, affine and metrical properties, covering both Euclidean and non-Euclidean geometries. With more than two thousand years of history, conic sections play a fundamental role in numerous fields of mathematics and physics, with applications to mechanical engineering, architecture, astronomy, design and computer graphics. This text will be invaluable to undergraduate mathematics students, those in adjacent fields of study, and anyone with an interest in classical geometry. Augmented with more than three hundred fifty figures and photographs, this innovative text will enhance your understanding of projective geometry, linear algebra, mechanics, and differential geometry, with careful exposition and many illustrative exercises.

Function Theory on Symplectic Manifolds

Author : Leonid Polterovich
Publisher : American Mathematical Soc.
ISBN 13 : 147041693X
Total Pages : 282 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Function Theory on Symplectic Manifolds by : Leonid Polterovich

Download or read book Function Theory on Symplectic Manifolds written by Leonid Polterovich and published by American Mathematical Soc.. This book was released on 2014 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book on symplectic topology, a rapidly developing field of mathematics which originated as a geometric tool for problems of classical mechanics. Since the 1980s, powerful methods such as Gromov's pseudo-holomorphic curves and Morse-Floer theory on loop spaces gave rise to the discovery of unexpected symplectic phenomena. The present book focuses on function spaces associated with a symplectic manifold. A number of recent advances show that these spaces exhibit intriguing properties and structures, giving rise to an alternative intuition and new tools in symplectic topology. The book provides an essentially self-contained introduction into these developments along with applications to symplectic topology, algebra and geometry of symplectomorphism groups, Hamiltonian dynamics and quantum mechanics. It will appeal to researchers and students from the graduate level onwards.

Advances in Functional Analysis and Operator Theory

Author : Marat V. Markin
Publisher : American Mathematical Society
ISBN 13 : 1470473054
Total Pages : 250 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Advances in Functional Analysis and Operator Theory by : Marat V. Markin

Download or read book Advances in Functional Analysis and Operator Theory written by Marat V. Markin and published by American Mathematical Society. This book was released on 2024-04-09 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS-EMS-SMF Special Session on Advances in Functional Analysis and Operator Theory, held July 18–22, 2022, at the Université de Grenoble-Alpes, Grenoble, France. The papers reflect the modern interplay between differential equations, functional analysis, operator algebras, and their applications from the dynamics to quantum groups to number theory. Among the topics discussed are the Sturm-Liouville and boundary value problems, axioms of quantum mechanics, $C^{*}$-algebras and symbolic dynamics, von Neumann algebras and low-dimensional topology, quantum permutation groups, the Jordan algebras, and the Kadison–Singer transforms.

Topology, Geometry, Integrable Systems, and Mathematical Physics

Author : V. M. Buchstaber
Publisher : American Mathematical Soc.
ISBN 13 : 1470418711
Total Pages : 408 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Topology, Geometry, Integrable Systems, and Mathematical Physics by : V. M. Buchstaber

Download or read book Topology, Geometry, Integrable Systems, and Mathematical Physics written by V. M. Buchstaber and published by American Mathematical Soc.. This book was released on 2014-11-18 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Articles in this collection are devoted to modern problems of topology, geometry, mathematical physics, and integrable systems, and they are based on talks given at the famous Novikov's seminar at the Steklov Institute of Mathematics in Moscow in 2012-2014. The articles cover many aspects of seemingly unrelated areas of modern mathematics and mathematical physics; they reflect the main scientific interests of the organizer of the seminar, Sergey Petrovich Novikov. The volume is suitable for graduate students and researchers interested in the corresponding areas of mathematics and physics.

Discrete Systems and Integrability

Author : J. Hietarinta
Publisher : Cambridge University Press
ISBN 13 : 1316654087
Total Pages : 461 pages
Book Rating : 4.3/5 (166 download)

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Book Synopsis Discrete Systems and Integrability by : J. Hietarinta

Download or read book Discrete Systems and Integrability written by J. Hietarinta and published by Cambridge University Press. This book was released on 2016-08-19 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elementary level, the book also highlights many recent developments. Topics include: Darboux and Bäcklund transformations; difference equations and special functions; multidimensional consistency of integrable lattice equations; associated linear problems (Lax pairs); connections with Padé approximants and convergence algorithms; singularities and geometry; Hirota's bilinear formalism for lattices; intriguing properties of discrete Painlevé equations; and the novel theory of Lagrangian multiforms. The book builds the material in an organic way, emphasizing interconnections between the various approaches, while the exposition is mostly done through explicit computations on key examples. Written by respected experts in the field, the numerous exercises and the thorough list of references will benefit upper-level undergraduate, and beginning graduate students as well as researchers from other disciplines.

Advances in Discrete Differential Geometry

Author : Alexander I. Bobenko
Publisher : Springer
ISBN 13 : 3662504472
Total Pages : 441 pages
Book Rating : 4.6/5 (625 download)

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Book Synopsis Advances in Discrete Differential Geometry by : Alexander I. Bobenko

Download or read book Advances in Discrete Differential Geometry written by Alexander I. Bobenko and published by Springer. This book was released on 2016-08-12 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, and on pure mathematics and its practical applications. The interaction of these facets is demonstrated by concrete examples, including discrete conformal mappings, discrete complex analysis, discrete curvatures and special surfaces, discrete integrable systems, conformal texture mappings in computer graphics, and free-form architecture. This richly illustrated book will convince readers that this new branch of mathematics is both beautiful and useful. It will appeal to graduate students and researchers in differential geometry, complex analysis, mathematical physics, numerical methods, discrete geometry, as well as computer graphics and geometry processing.

From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory

Author : Fritz Gesztesy
Publisher : Springer Nature
ISBN 13 : 3030754251
Total Pages : 388 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory by : Fritz Gesztesy

Download or read book From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory written by Fritz Gesztesy and published by Springer Nature. This book was released on 2021-11-11 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main topics of this volume, dedicated to Lance Littlejohn, are operator and spectral theory, orthogonal polynomials, combinatorics, number theory, and the various interplays of these subjects. Although the event, originally scheduled as the Baylor Analysis Fest, had to be postponed due to the pandemic, scholars from around the globe have contributed research in a broad range of mathematical fields. The collection will be of interest to both graduate students and professional mathematicians. Contributors are: G.E. Andrews, B.M. Brown, D. Damanik, M.L. Dawsey, W.D. Evans, J. Fillman, D. Frymark, A.G. García, L.G. Garza, F. Gesztesy, D. Gómez-Ullate, Y. Grandati, F.A. Grünbaum, S. Guo, M. Hunziker, A. Iserles, T.F. Jones, K. Kirsten, Y. Lee, C. Liaw, F. Marcellán, C. Markett, A. Martinez-Finkelshtein, D. McCarthy, R. Milson, D. Mitrea, I. Mitrea, M. Mitrea, G. Novello, D. Ong, K. Ono, J.L. Padgett, M.M.M. Pang, T. Poe, A. Sri Ranga, K. Schiefermayr, Q. Sheng, B. Simanek, J. Stanfill, L. Velázquez, M. Webb, J. Wilkening, I.G. Wood, M. Zinchenko.

Hamiltonian Systems

Author : Albert Fathi
Publisher : Cambridge University Press
ISBN 13 : 1009320718
Total Pages : 377 pages
Book Rating : 4.0/5 (93 download)

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Book Synopsis Hamiltonian Systems by : Albert Fathi

Download or read book Hamiltonian Systems written by Albert Fathi and published by Cambridge University Press. This book was released on 2024-05-31 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: A selection of results, spanning a broad spectrum of disciplines, from the MSRI program on Hamiltonian Systems during Fall 2018.

Geometry and Billiards

Author : Serge Tabachnikov
Publisher : American Mathematical Soc.
ISBN 13 : 0821839195
Total Pages : 192 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Geometry and Billiards by : Serge Tabachnikov

Download or read book Geometry and Billiards written by Serge Tabachnikov and published by American Mathematical Soc.. This book was released on 2005 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. Topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards. The book is based on an advanced undergraduate topics course. Minimum prerequisites are the standard material covered in the first two years of college mathematics (the entire calculus sequence, linear algebra). However, readers should show some mathematical maturity and rely on their mathematical common sense. A unique feature of the book is the coverage of many diverse topics related to billiards, for example, evolutes and involutes of plane curves, the four-vertex theorem, a mathematical theory of rainbows, distribution of first digits in various sequences, Morse theory, the Poincare recurrence theorem, Hilbert's fourth problem, Poncelet porism, and many others. There are approximately 100 illustrations. The book is suitable for advanced undergraduates, graduate students, and researchers interested in ergodic theory and geometry. This volume has been copublished with the Mathematics Advanced Study Semesters program at Penn State.

The History of Mathematical Proof in Ancient Traditions

Author : Karine Chemla
Publisher : Cambridge University Press
ISBN 13 : 1139510584
Total Pages : pages
Book Rating : 4.1/5 (395 download)

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Book Synopsis The History of Mathematical Proof in Ancient Traditions by : Karine Chemla

Download or read book The History of Mathematical Proof in Ancient Traditions written by Karine Chemla and published by Cambridge University Press. This book was released on 2012-07-05 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This radical, profoundly scholarly book explores the purposes and nature of proof in a range of historical settings. It overturns the view that the first mathematical proofs were in Greek geometry and rested on the logical insights of Aristotle by showing how much of that view is an artefact of nineteenth-century historical scholarship. It documents the existence of proofs in ancient mathematical writings about numbers and shows that practitioners of mathematics in Mesopotamian, Chinese and Indian cultures knew how to prove the correctness of algorithms, which are much more prominent outside the limited range of surviving classical Greek texts that historians have taken as the paradigm of ancient mathematics. It opens the way to providing the first comprehensive, textually based history of proof.

5000 Years of Geometry

Author : Christoph J. Scriba
Publisher : Birkhäuser
ISBN 13 : 3034808984
Total Pages : 638 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis 5000 Years of Geometry by : Christoph J. Scriba

Download or read book 5000 Years of Geometry written by Christoph J. Scriba and published by Birkhäuser. This book was released on 2015-04-22 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume provides a fascinating overview of geometrical ideas and perceptions from the earliest cultures to the mathematical and artistic concepts of the 20th century. It is the English translation of the 3rd edition of the well-received German book “5000 Jahre Geometrie,” in which geometry is presented as a chain of developments in cultural history and their interaction with architecture, the visual arts, philosophy, science and engineering. Geometry originated in the ancient cultures along the Indus and Nile Rivers and in Mesopotamia, experiencing its first “Golden Age” in Ancient Greece. Inspired by the Greek mathematics, a new germ of geometry blossomed in the Islamic civilizations. Through the Oriental influence on Spain, this knowledge later spread to Western Europe. Here, as part of the medieval Quadrivium, the understanding of geometry was deepened, leading to a revival during the Renaissance. Together with parallel achievements in India, China, Japan and the ancient American cultures, the European approaches formed the ideas and branches of geometry we know in the modern age: coordinate methods, analytical geometry, descriptive and projective geometry in the 17th an 18th centuries, axiom systems, geometry as a theory with multiple structures and geometry in computer sciences in the 19th and 20th centuries. Each chapter of the book starts with a table of key historical and cultural dates and ends with a summary of essential contents of geometr y in the respective era. Compelling examples invite the reader to further explore the problems of geometry in ancient and modern times. The book will appeal to mathematicians interested in Geometry and to all readers with an interest in cultural history. From letters to the authors for the German language edition I hope it gets a translation, as there is no comparable work. Prof. J. Grattan-Guinness (Middlesex University London) "Five Thousand Years of Geometry" - I think it is the most handsome book I have ever seen from Springer and the inclusion of so many color plates really improves its appearance dramatically! Prof. J.W. Dauben (City University of New York) An excellent book in every respect. The authors have successfully combined the history of geometry with the general development of culture and history. ... The graphic design is also excellent. Prof. Z. Nádenik (Czech Technical University in Prague)