Tag: Geometry

Free Download Solving Problems In Point Geometry: Insights And Strategies For Mathematical Olympiad And Competitions
English | 2025 | ISBN: 9811294100 | 235 Pages | PDF (True) | 12 MB
For over two millennia, the complexities of elementary geometry have challenged learners, burdened by the intricacies of auxiliary graphics and cumbersome calculations. Inspired by Leibniz’s query, this book introduces a groundbreaking method: point geometry. By operating directly on points, it integrates the strengths of coordinate, vector, and mass point methods, simplifying operations and problem-solving.Central to this method is the identity approach, which streamlines complex problems into concise equations, unlocking multiple propositions with ease. Through meticulously crafted examples, readers are invited to explore the joy of mathematical thinking.Beyond mathematics, point geometry holds promise for artificial intelligence, offering a simple yet rich knowledge representation and reasoning method. With most solutions generated by computer programs, the potential for simplifying reasoning methods is immense, paving the way for a brighter future in both education and AI advancement.In this ambitious endeavor, the authors seek to simplify knowledge representation and reasoning, reduce the burden of learning, and accelerate the progress of artificial intelligence. This book is not just a guide to geometry; it’s a catalyst for transformative thinking and discovery.

Free Download Tushar Das, David Simmons, Mariusz Urbanski, "Geometry and Dynamics in Gromov Hyperbolic Metric Spaces: With an Emphasis on Non-proper Settings"
English | 2017 | ISBN: 1470434652 | PDF | pages: 321 | 4.0 mb
This book presents the foundations of the theory of groups and semigroups acting isometrically on Gromov hyperbolic metric spaces. Particular emphasis is paid to the geometry of their limit sets and on behavior not found in the proper setting. The authors provide a number of examples of groups which exhibit a wide range of phenomena not to be found in the finite-dimensional theory. The book contains both introductory material to help beginners as well as new research results, and closes with a list of attractive unsolved problems.

Free Download Noncommutative Geometry and Particle Physics
English | 2025 | ISBN: 3031591194 | 328 Pages | PDF EPUB (True) | 29 MB
This book provides an introduction to noncommutative geometry and presents a number of its recent applications to particle physics. In the first part, we introduce the main concepts and techniques by studying finite noncommutative spaces, providing a "light" approach to noncommutative geometry. We then proceed with the general framework by defining and analyzing noncommutative spin manifolds and deriving some main results on them, such as the local index formula. In the second part, we show how noncommutative spin manifolds naturally give rise to gauge theories, applying this principle to specific examples. We subsequently geometrically derive abelian and non-abelian Yang-Mills gauge theories, and eventually the full Standard Model of particle physics, and conclude by explaining how noncommutative geometry might indicate how to proceed beyond the Standard Model.

Free Download The Man Who Saved Geometry: The Multidimensional Mind of Donald Coxeter by Siobhan Roberts
English | October 29, 2024 | ISBN: 0691264740 | 416 pages | PDF | 57 Mb
An illuminating biography of one of the greatest geometers of the twentieth century

Free Download New Developments in Differential Geometry: Proceedings of the Colloquium on Differential Geometry, Debrecen, Hungary,July 26-30, 1994 By D. V. Alekseevsky, S. Marchiafava (auth.), L. Tamássy, J. Szenthe (eds.)
1996 | 437 Pages | ISBN: 9401065535 | PDF | 11 MB
This volume contains thirty-six research articles presented at the Colloquium on Differential Geometry, which was held in Debrecen, Hungary, July 26-30, 1994. The conference was a continuation in the series of the Colloquia of the János Bolyai Society. The range covered reflects current activity in differential geometry. The main topics are Riemannian geometry, Finsler geometry, submanifold theory and applications to theoretical physics. Includes several interesting results by leading researchers in these fields: e.g. on non-commutative geometry, spin bordism groups, Cosserat continuum, field theories, second order differential equations, sprays, natural operators, higher order frame bundles, Sasakian and Kähler manifolds. Audience: This book will be valuable for researchers and postgraduate students whose work involves differential geometry, global analysis, analysis on manifolds, relativity and gravitation and electromagnetic theory.

Free Download Geometry, Topology and Quantization By Pratul Bandyopadhyay (auth.)
1996 | 230 Pages | ISBN: 940106282X | PDF | 19 MB
This is a monograph on geometrical and topological features which arise in various quantization procedures. Quantization schemes consider the feasibility of arriving at a quantum system from a classical one and these involve three major procedures viz. i) geometric quantization, ii) Klauder quantization, and iii) stochastic quanti zation. In geometric quantization we have to incorporate a hermitian line bundle to effectively generate the quantum Hamiltonian operator from a classical Hamil tonian. Klauder quantization also takes into account the role of the connection one-form along with coordinate independence. In stochastic quantization as pro posed by Nelson, Schrodinger equation is derived from Brownian motion processes; however, we have difficulty in its relativistic generalization. It has been pointed out by several authors that this may be circumvented by formulating a new geometry where Brownian motion proceses are considered in external as well as in internal space and, when the complexified space-time is considered, the usual path integral formulation is achieved. When this internal space variable is considered as a direc tion vector introducing an anisotropy in the internal space, we have the quantization of a Fermi field. This helps us to formulate a stochastic phase space formalism when the internal extension can be treated as a gauge theoretic extension. This suggests that massive fermions may be considered as Skyrme solitons. The nonrelativistic quantum mechanics is achieved in the sharp point limit.

Free Download Geometry Workbook For Dummies, 2nd Edition by Mark Ryan
English | November 13, 2024 | ISBN: 1394276125 | True PDF | 336 pages | 18 MB
Don’t be a square! Strengthen your geometrical skills

Free Download Canonical Metrics in Kähler Geometry by Gang Tian
English | PDF | 2000 | 107 Pages | ISBN : 3764361948 | 6.8 MB
There has been fundamental progress in complex differential geometry in the last two decades. For one, The uniformization theory of canonical Kähler metrics has been established in higher dimensions, and many applications have been found, including the use of Calabi-Yau spaces in superstring theory. This monograph gives an introduction to the theory of canonical Kähler metrics on complex manifolds. It also presents some advanced topics not easily found elsewhere.

Free Download Introduction to Hyperbolic Geometry By Arlan Ramsay, Robert D. Richtmyer (auth.)
1995 | 289 Pages | ISBN: 0387943390 | PDF | 13 MB
This book is an introduction to hyperbolic and differential geometry that provides material in the early chapters that can serve as a textbook for a standard upper division course on hyperbolic geometry. For that material, the students need to be familiar with calculus and linear algebra and willing to accept one advanced theorem from analysis without proof. The book goes well beyond the standard course in later chapters, and there is enough material for an honors course, or for supplementary reading. Indeed, parts of the book have been used for both kinds of courses. Even some of what is in the early chapters would surely not be nec essary for a standard course. For example, detailed proofs are given of the Jordan Curve Theorem for Polygons and of the decomposability of poly gons into triangles, These proofs are included for the sake of completeness, but the results themselves are so believable that most students should skip the proofs on a first reading. The axioms used are modern in character and more "user friendly" than the traditional ones. The familiar real number system is used as an in gredient rather than appearing as a result of the axioms. However, it should not be thought that the geometric treatment is in terms of models: this is an axiomatic approach that is just more convenient than the traditional ones.

Free Download Geometry of Submanifolds and Applications (Infosys Science Foundation Series) by Bang-Yen Chen, Majid Ali Choudhary, Mohammad Nazrul Islam Khan
English | March 27, 2024 | ISBN: 9819997496 | 234 pages | MOBI | 38 Mb
This book features chapters written by renowned scientists from various parts of the world, providing an up-to-date survey of submanifold theory, spanning diverse topics and applications. The book covers a wide range of topics such as Chen-Ricci inequalities in differential geometry, optimal inequalities for Casorati curvatures in quaternion geometry, conformal η-Ricci-Yamabe solitons, submersion on statistical metallic structure, solitons in f(R, T)-gravity, metric-affine geometry, generalized Wintgen inequalities, tangent bundles, and Lagrangian submanifolds.