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Barycentric Calculus In Euclidean And Hyperbolic Geometry
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Book Synopsis Barycentric Calculus in Euclidean and Hyperbolic Geometry by : Abraham A. Ungar
Download or read book Barycentric Calculus in Euclidean and Hyperbolic Geometry written by Abraham A. Ungar and published by World Scientific. This book was released on 2010 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: The word barycentric is derived from the Greek word barys (heavy), and refers to center of gravity. Barycentric calculus is a method of treating geometry by considering a point as the center of gravity of certain other points to which weights are ascribed. Hence, in particular, barycentric calculus provides excellent insight into triangle centers. This unique book on barycentric calculus in Euclidean and hyperbolic geometry provides an introduction to the fascinating and beautiful subject of novel triangle centers in hyperbolic geometry along with analogies they share with familiar triangle centers in Euclidean geometry. As such, the book uncovers magnificent unifying notions that Euclidean and hyperbolic triangle centers share. In his earlier books the author adopted Cartesian coordinates, trigonometry and vector algebra for use in hyperbolic geometry that is fully analogous to the common use of Cartesian coordinates, trigonometry and vector algebra in Euclidean geometry. As a result, powerful tools that are commonly available in Euclidean geometry became available in hyperbolic geometry as well, enabling one to explore hyperbolic geometry in novel ways. In particular, this new book establishes hyperbolic barycentric coordinates that are used to determine various hyperbolic triangle centers just as Euclidean barycentric coordinates are commonly used to determine various Euclidean triangle centers. The hunt for Euclidean triangle centers is an old tradition in Euclidean geometry, resulting in a repertoire of more than three thousand triangle centers that are known by their barycentric coordinate representations. The aim of this book is to initiate a fully analogous hunt for hyperbolic triangle centers that will broaden the repertoire of hyperbolic triangle centers provided here.
Book Synopsis Euclidean and Non-Euclidean Geometry International Student Edition by : Patrick J. Ryan
Download or read book Euclidean and Non-Euclidean Geometry International Student Edition written by Patrick J. Ryan and published by Cambridge University Press. This book was released on 2009-09-04 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a rigorous treatment of the fundamentals of plane geometry: Euclidean, spherical, elliptical and hyperbolic.
Book Synopsis Analytic Hyperbolic Geometry in N Dimensions by : Abraham Albert Ungar
Download or read book Analytic Hyperbolic Geometry in N Dimensions written by Abraham Albert Ungar and published by CRC Press. This book was released on 2014-12-17 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of the Euclidean simplex is important in the study of n-dimensional Euclidean geometry. This book introduces for the first time the concept of hyperbolic simplex as an important concept in n-dimensional hyperbolic geometry. Following the emergence of his gyroalgebra in 1988, the author crafted gyrolanguage, the algebraic language t
Book Synopsis Analytic Hyperbolic Geometry And Albert Einstein's Special Theory Of Relativity (Second Edition) by : Abraham Albert Ungar
Download or read book Analytic Hyperbolic Geometry And Albert Einstein's Special Theory Of Relativity (Second Edition) written by Abraham Albert Ungar and published by World Scientific. This book was released on 2022-02-22 with total page 775 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a powerful way to study Einstein's special theory of relativity and its underlying hyperbolic geometry in which analogies with classical results form the right tool. The premise of analogy as a study strategy is to make the unfamiliar familiar. Accordingly, this book introduces the notion of vectors into analytic hyperbolic geometry, where they are called gyrovectors. Gyrovectors turn out to be equivalence classes that add according to the gyroparallelogram law just as vectors are equivalence classes that add according to the parallelogram law. In the gyrolanguage of this book, accordingly, one prefixes a gyro to a classical term to mean the analogous term in hyperbolic geometry. As an example, the relativistic gyrotrigonometry of Einstein's special relativity is developed and employed to the study of the stellar aberration phenomenon in astronomy.Furthermore, the book presents, for the first time, the relativistic center of mass of an isolated system of noninteracting particles that coincided at some initial time t = 0. It turns out that the invariant mass of the relativistic center of mass of an expanding system (like galaxies) exceeds the sum of the masses of its constituent particles. This excess of mass suggests a viable mechanism for the formation of dark matter in the universe, which has not been detected but is needed to gravitationally 'glue' each galaxy in the universe. The discovery of the relativistic center of mass in this book thus demonstrates once again the usefulness of the study of Einstein's special theory of relativity in terms of its underlying hyperbolic geometry.
Book Synopsis Essays in Mathematics and its Applications by : Themistocles M. Rassias
Download or read book Essays in Mathematics and its Applications written by Themistocles M. Rassias and published by Springer. This book was released on 2016-06-14 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, dedicated to the eminent mathematician Vladimir Arnold, presents a collection of research and survey papers written on a large spectrum of theories and problems that have been studied or introduced by Arnold himself. Emphasis is given to topics relating to dynamical systems, stability of integrable systems, algebraic and differential topology, global analysis, singularity theory and classical mechanics. A number of applications of Arnold’s groundbreaking work are presented. This publication will assist graduate students and research mathematicians in acquiring an in-depth understanding and insight into a wide domain of research of an interdisciplinary nature.
Book Synopsis Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces by : Abraham Ungar
Download or read book Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces written by Abraham Ungar and published by Academic Press. This book was released on 2018-01-10 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces presents for the first time a unified study of the Lorentz transformation group SO(m, n) of signature (m, n), m, n ? N, which is fully analogous to the Lorentz group SO(1, 3) of Einstein’s special theory of relativity. It is based on a novel parametric realization of pseudo-rotations by a vector-like parameter with two orientation parameters. The book is of interest to specialized researchers in the areas of algebra, geometry and mathematical physics, containing new results that suggest further exploration in these areas. Introduces the study of generalized gyrogroups and gyrovector spaces Develops new algebraic structures, bi-gyrogroups and bi-gyrovector spaces Helps readers to surmount boundaries between algebra, geometry and physics Assists readers to parametrize and describe the full set of generalized Lorentz transformations in a geometric way Generalizes approaches from gyrogroups and gyrovector spaces to bi-gyrogroups and bi-gyrovector spaces with geometric entanglement
Book Synopsis Nonlinear Analysis by : Panos M. Pardalos
Download or read book Nonlinear Analysis written by Panos M. Pardalos and published by Springer Science & Business Media. This book was released on 2012-06-02 with total page 898 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume will consist of about 40 articles written by some very influential mathematicians of our time and will expose the latest achievements in the broad area of nonlinear analysis and its various interdisciplinary applications.
Book Synopsis Essays in Mathematics and its Applications by : Panos M. Pardalos
Download or read book Essays in Mathematics and its Applications written by Panos M. Pardalos and published by Springer Science & Business Media. This book was released on 2012-08-07 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume is dedicated to Stephen Smale on the occasion of his 80th birthday.Besides his startling 1960 result of the proof of the Poincar ́e conjecture for all dimensionsgreater than or equal to five, Smale’s ground breaking contributions invarious fields in Mathematics have marked the second part of the 20th century andbeyond. Stephen Smale has done pioneering work in differential topology, globalanalysis, dynamical systems, nonlinear functional analysis, numerical analysis, theoryof computation and machine learning as well as applications in the physical andbiological sciences and economics. In sum, Stephen Smale has manifestly brokenthe barriers among the different fields of mathematics and dispelled some remainingprejudices. He is indeed a universal mathematician. Smale has been honoredwith several prizes and honorary degrees including, among others, the Fields Medal(1966), The Veblen Prize (1966), the National Medal of Science (1996) and theWolfPrize (2006/2007).
Book Synopsis Problems and Recent Methods in Operator Theory by : Fernanda Botelho
Download or read book Problems and Recent Methods in Operator Theory written by Fernanda Botelho and published by American Mathematical Soc.. This book was released on 2017-04-18 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Workshop on Problems and Recent Methods in Operator Theory, held at the University of Memphis, Memphis, TN, from October 15–16, 2015 and the AMS Special Session on Advances in Operator Theory and Applications, in Memory of James Jamison, held at the University of Memphis, Memphis, TN, from October 17–18, 2015. Operator theory is at the root of several branches of mathematics and offers a broad range of challenging and interesting research problems. It also provides powerful tools for the development of other areas of science including quantum theory, physics and mechanics. Isometries have applications in solid-state physics. Hermitian operators play an integral role in quantum mechanics very much due to their “nice” spectral properties. These powerful connections demonstrate the impact of operator theory in various branches of science. The articles in this volume address recent problems and research advances in operator theory. Highlighted topics include spectral, structural and geometric properties of special types of operators on Banach spaces, with emphasis on isometries, weighted composition operators, multi-circular projections on function spaces, as well as vector valued function spaces and spaces of analytic functions. This volume gives a succinct overview of state-of-the-art techniques from operator theory as well as applications to classical problems and long-standing open questions.
Book Synopsis Mathematics Without Boundaries by : Themistocles M. Rassias
Download or read book Mathematics Without Boundaries written by Themistocles M. Rassias and published by Springer. This book was released on 2014-09-17 with total page 783 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions in this volume have been written by eminent scientists from the international mathematical community and present significant advances in several theories, methods and problems of Mathematical Analysis, Discrete Mathematics, Geometry and their Applications. The chapters focus on both old and recent developments in Functional Analysis, Harmonic Analysis, Complex Analysis, Operator Theory, Combinatorics, Functional Equations, Differential Equations as well as a variety of Applications. The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical Sciences, and especially to graduate students looking for the latest information.
Book Synopsis Three Plays of Maureen Hunter by : Hunter, Maureen
Download or read book Three Plays of Maureen Hunter written by Hunter, Maureen and published by OIBooks-Libros. This book was released on 2003 with total page 944 pages. Available in PDF, EPUB and Kindle. Book excerpt: Book is clean and tight. No writing in text. Like New
Book Synopsis Advances in Knowledge Discovery and Data Mining by : De-Nian Yang
Download or read book Advances in Knowledge Discovery and Data Mining written by De-Nian Yang and published by Springer Nature. This book was released on with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Proceedings of 10th International Conference on Recent Advances in Civil Aviation by : Oleg Anatolyevich Gorbachev
Download or read book Proceedings of 10th International Conference on Recent Advances in Civil Aviation written by Oleg Anatolyevich Gorbachev and published by Springer Nature. This book was released on 2022-10-19 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume comprises proceedings of the 10th International Conference on Recent Advances in Civil Aviation. The contents focus on air traffic control and management, quality control and reliability improvement of radio equipment and avionics, designing and testing aircraft assemblies and mechanisms, reliability improvement of aircraft management systems, aviation enterprise management, etc. There is also emphasis on the current problems and prospects for development of unmanned aircraft systems. This volume will be beneficial to researchers, practitioners, and policy-makers alike.
Book Synopsis Complex Networks XIV by : Andreia Sofia Teixeira
Download or read book Complex Networks XIV written by Andreia Sofia Teixeira and published by Springer Nature. This book was released on 2023-03-29 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains contributions in the area of Network Science, presented at the 14th International Conference on Complex Networks (CompleNet), 24-28 April, 2023 in Aveiro, Portugal. CompleNet is an international conference on complex networks that brings together researchers and practitioners from diverse disciplines—from sociology, biology, physics, and computer science—who share a passion to better understand the interdependencies within and across systems. CompleNet is a venue to discuss ideas and findings about all types networks, from biological, to technological, to informational and social. It is this interdisciplinary nature of complex networks that CompleNet aims to explore and celebrate. The audience of the work are professionals and academics working in Network Science, a highly-multidisciplinary field.
Book Synopsis Old and New Topics in Geometry by : Franz Rothe
Download or read book Old and New Topics in Geometry written by Franz Rothe and published by Litprime Solutions. This book was released on 2022-09-28 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A decade long experience of teaching the course "Fundamental of Geometry", many notes for exercises, and endless extra reading are the bases for this bulky work. The online manuscript already includes many topics with many exercises including solutions and hundreds a elaborate computer generated drawings. The first volume begins with Hilbert's axioms from the Foundations of Geometry, and goes on to projective, neutral and basic Euclidean geometry. The present second volume deals with many more advanced topics form Euclidean geometry and contains a long treatise about hyperbolic geometry. Here the disk models of Poincar\'e and Klein are used to do a lot of constructions, using straightedge and compass from the background Euclidean geometry. Too, Hilbert's axiomatic approach based on the asymptotic rays, is explained from the beginning up to the reconstruction of the Poincar\'e disk model. The last section gives a short course on Gauss' differential geometry and the pseudo sphere.
Book Synopsis Mathematics and Theoretical Physics by : Minaketan Behara
Download or read book Mathematics and Theoretical Physics written by Minaketan Behara and published by Walter de Gruyter. This book was released on 2011-06-15 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Book Synopsis Mathematics Without Boundaries by : Panos M. Pardalos
Download or read book Mathematics Without Boundaries written by Panos M. Pardalos and published by Springer. This book was released on 2014-09-16 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of chapters written by eminent scientists and engineers from the international community and present significant advances in several theories, methods and applications of an interdisciplinary research. These contributions focus on both old and recent developments of Global Optimization Theory, Convex Analysis, Calculus of Variations, Discrete Mathematics and Geometry, as well as several applications to a large variety of concrete problems, including applications of computers to the study of smoothness and analyticity of functions, applications to epidemiological diffusion, networks, mathematical models of elastic and piezoelectric fields, optimal algorithms, stability of neutral type vector functional differential equations, sampling and rational interpolation for non-band-limited signals, recurrent neural network for convex optimization problems and experimental design. The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical and Engineering subjects and especially to graduate students who search for the latest information.
