Download or read book Basic Lessons On Isometries Similarities And Inversions In The Euclidean Plane A Synthetic Approach written by Ioannis Markos Roussos and published by World Scientific. This book was released on 2021-09-03 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to provide a complete synthetic exposition of plane isometries, similarities and inversions to readers who are interested in studying, teaching, and using this material.The topics developed in this book can provide new proofs and solutions to many results and problems of classical geometry, which are presented with different proofs in the literature. Their applications are numerous and some, such as the Steiner Chains and Point, are useful to engineers.The book contains many good examples, important applications and numerous exercises of various level and difficulty, which are classified in the three groups of: general exercises, geometrical constructions, and geometrical loci. Some lengthy exercises or groups of related exercises can be viewed as projects. On the basis of the above, this book, besides Classical Geometry, is an important addition to Mathematics Education.
Download or read book Geometric Transformations written by Răzvan Gelca and published by Springer Nature. This book was released on 2022-02-16 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook teaches the transformations of plane Euclidean geometry through problems, offering a transformation-based perspective on problems that have appeared in recent years at mathematics competitions around the globe, as well as on some classical examples and theorems. It is based on the combined teaching experience of the authors (coaches of several Mathematical Olympiad teams in Brazil, Romania and the USA) and presents comprehensive theoretical discussions of isometries, homotheties and spiral similarities, and inversions, all illustrated by examples and followed by myriad problems left for the reader to solve. These problems were carefully selected and arranged to introduce students to the topics by gradually moving from basic to expert level. Most of them have appeared in competitions such as Mathematical Olympiads or in mathematical journals aimed at an audience interested in mathematics competitions, while some are fundamental facts of mathematics discussed in the framework of geometric transformations. The book offers a global view of the geometric content of today's mathematics competitions, bringing many new methods and ideas to the attention of the public. Talented high school and middle school students seeking to improve their problem-solving skills can benefit from this book, as well as high school and college instructors who want to add nonstandard questions to their courses. People who enjoy solving elementary math problems as a hobby will also enjoy this work.
Download or read book Geometry Illuminated written by Matthew Harvey and published by The Mathematical Association of America. This book was released on 2015-09-25 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry Illuminated is an introduction to geometry in the plane, both Euclidean and hyperbolic. It is designed to be used in an undergraduate course on geometry, and as such, its target audience is undergraduate math majors. However, much of it should be readable by anyone who is comfortable with the language of mathematical proof. Throughout, the goal is to develop the material patiently. One of the more appealing aspects of geometry is that it is a very "visual" subject. This book hopes to takes full advantage of that, with an extensive use of illustrations as guides. Geometry Illuminated is divided into four principal parts. Part 1 develops neutral geometry in the style of Hilbert, including a discussion of the construction of measure in that system, ultimately building up to the Saccheri-Legendre Theorem. Part 2 provides a glimpse of classical Euclidean geometry, with an emphasis on concurrence results, such as the nine-point circle. Part 3 studies transformations of the Euclidean plane, beginning with isometries and ending with inversion, with applications and a discussion of area in between. Part 4 is dedicated to the development of the Poincaré disk model, and the study of geometry within that model. While this material is traditional, Geometry Illuminated does bring together topics that are generally not found in a book at this level. Most notably, it explicitly computes parametric equations for the pseudosphere and its geodesics. It focuses less on the nature of axiomatic systems for geometry, but emphasizes rather the logical development of geometry within such a system. It also includes sections dealing with trilinear and barycentric coordinates, theorems that can be proved using inversion, and Euclidean and hyperbolic tilings.
Download or read book Transformation Geometry written by Jagat Narain Kapur and published by . This book was released on 1976 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometries written by Alekseĭ Bronislavovich Sosinskiĭ and published by American Mathematical Soc.. This book was released on 2012 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to the proposition that all geometries are created equal--although some, of course, remain more equal than others. The author concentrates on several of the more distinguished and beautiful ones, which include what he terms ``toy geometries'', the geometries of Platonic bodies, discrete geometries, and classical continuous geometries. The text is based on first-year semester course lectures delivered at the Independent University of Moscow in 2003 and 2006. It is by no means a formal algebraic or analytic treatment of geometric topics, but rather, a highly visual exposition containing upwards of 200 illustrations. The reader is expected to possess a familiarity with elementary Euclidean geometry, albeit those lacking this knowledge may refer to a compendium in Chapter 0. Per the author's predilection, the book contains very little regarding the axiomatic approach to geometry (save for a single chapter on the history of non-Euclidean geometry), but two Appendices provide a detailed treatment of Euclid's and Hilbert's axiomatics. Perhaps the most important aspect of this course is the problems, which appear at the end of each chapter and are supplemented with answers at the conclusion of the text. By analyzing and solving these problems, the reader will become capable of thinking and working geometrically, much more so than by simply learning the theory. Ultimately, the author makes the distinction between concrete mathematical objects called ``geometries'' and the singular ``geometry'', which he understands as a way of thinking about mathematics. Although the book does not address branches of mathematics and mathematical physics such as Riemannian and Kahler manifolds or, say, differentiable manifolds and conformal field theories, the ideology of category language and transformation groups on which the book is based prepares the reader for the study of, and eventually, research in these important and rapidly developing areas of contemporary mathematics.
Download or read book Variations on a Theme of Borel written by Shmuel Weinberger and published by Cambridge University Press. This book was released on 2022-12-08 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the middle of the last century, after hearing a talk of Mostow on one of his rigidity theorems, Borel conjectured in a letter to Serre a purely topological version of rigidity for aspherical manifolds (i.e. manifolds with contractible universal covers). The Borel conjecture is now one of the central problems of topology with many implications for manifolds that need not be aspherical. Since then, the theory of rigidity has vastly expanded in both precision and scope. This book rethinks the implications of accepting his heuristic as a source of ideas. Doing so leads to many variants of the original conjecture - some true, some false, and some that remain conjectural. The author explores this collection of ideas, following them where they lead whether into rigidity theory in its differential geometric and representation theoretic forms, or geometric group theory, metric geometry, global analysis, algebraic geometry, K-theory, or controlled topology.
Download or read book Perspectives on the Teaching of Geometry for the 21st Century written by C. Mammana and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years geometry seems to have lost large parts of its former central position in mathematics teaching in most countries. However, new trends have begun to counteract this tendency. There is an increasing awareness that geometry plays a key role in mathematics and learning mathematics. Although geometry has been eclipsed in the mathematics curriculum, research in geometry has blossomed as new ideas have arisen from inside mathematics and other disciplines, including computer science. Due to reassessment of the role of geometry, mathematics educators and mathematicians face new challenges. In the present ICMI study, the whole spectrum of teaching and learning of geometry is analysed. Experts from all over the world took part in this study, which was conducted on the basis of recent international research, case studies, and reports on actual school practice. This book will be of particular interest to mathematics educators and mathematicians who are involved in the teaching of geometry at all educational levels, as well as to researchers in mathematics education.
Download or read book Exploring Geometry written by Michael Hvidsten and published by CRC Press. This book was released on 2016-12-08 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring Geometry, Second Edition promotes student engagement with the beautiful ideas of geometry. Every major concept is introduced in its historical context and connects the idea with real-life. A system of experimentation followed by rigorous explanation and proof is central. Exploratory projects play an integral role in this text. Students develop a better sense of how to prove a result and visualize connections between statements, making these connections real. They develop the intuition needed to conjecture a theorem and devise a proof of what they have observed. Features: Second edition of a successful textbook for the first undergraduate course Every major concept is introduced in its historical context and connects the idea with real life Focuses on experimentation Projects help enhance student learning All major software programs can be used; free software from author
Download or read book Geometry III written by Yu.D. Burago and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: A volume devoted to the extremely clear and intrinsically beautiful theory of two-dimensional surfaces in Euclidean spaces. The main focus is on the connection between the theory of embedded surfaces and two-dimensional Riemannian geometry, and the influence of properties of intrinsic metrics on the geometry of surfaces.
Download or read book Methods of Geometry written by James T. Smith and published by John Wiley & Sons. This book was released on 2011-03-01 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical, accessible introduction to advanced geometryExceptionally well-written and filled with historical andbibliographic notes, Methods of Geometry presents a practical andproof-oriented approach. The author develops a wide range ofsubject areas at an intermediate level and explains how theoriesthat underlie many fields of advanced mathematics ultimately leadto applications in science and engineering. Foundations, basicEuclidean geometry, and transformations are discussed in detail andapplied to study advanced plane geometry, polyhedra, isometries,similarities, and symmetry. An excellent introduction to advancedconcepts as well as a reference to techniques for use inindependent study and research, Methods of Geometry alsofeatures: Ample exercises designed to promote effective problem-solvingstrategies Insight into novel uses of Euclidean geometry More than 300 figures accompanying definitions and proofs A comprehensive and annotated bibliography Appendices reviewing vector and matrix algebra, least upperbound principle, and equivalence relations An Instructor's Manual presenting detailed solutions to all theproblems in the book is available upon request from the Wileyeditorial department.
Download or read book Discovering Geometry written by Michael Serra and published by . This book was released on 2003-03-01 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Treatise of Plane Geometry Through Geometric Algebra written by Ramón González Calvet and published by Treatise of Plane Geometry. This book was released on 2007 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometry of Surfaces written by John Stillwell and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: The geometry of surfaces is an ideal starting point for learning geometry, for, among other reasons, the theory of surfaces of constant curvature has maximal connectivity with the rest of mathematics. This text provides the student with the knowledge of a geometry of greater scope than the classical geometry taught today, which is no longer an adequate basis for mathematics or physics, both of which are becoming increasingly geometric. It includes exercises and informal discussions.
Download or read book Notes on Geometry written by Elmer G. Rees and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, geometry has played a lesser role in undergraduate courses than it has ever done. Nevertheless, it still plays a leading role in mathematics at a higher level. Its central role in the history of mathematics has never been disputed. It is important, therefore, to introduce some geometry into university syllabuses. There are several ways of doing this, it can be incorporated into existing courses that are primarily devoted to other topics, it can be taught at a first year level or it can be taught in higher level courses devoted to differential geometry or to more classical topics. These notes are intended to fill a rather obvious gap in the literature. It treats the classical topics of Euclidean, projective and hyperbolic geometry but uses the material commonly taught to undergraduates: linear algebra, group theory, metric spaces and complex analysis. The notes are based on a course whose aim was two fold, firstly, to introduce the students to some geometry and secondly to deepen their understanding of topics that they have already met. What is required from the earlier material is a familiarity with the main ideas, specific topics that are used are usually redone.
Download or read book Structure and Equivalence written by Neil Dewar and published by Cambridge University Press. This book was released on 2022-03-17 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Element explores what it means for two theories in physics to be equivalent (or inequivalent), and what lessons can be drawn about their structure as a result. It does so through a twofold approach. On the one hand, it provides a synoptic overview of the logical tools that have been employed in recent philosophy of physics to explore these topics: definition, translation, Ramsey sentences, and category theory. On the other, it provides a detailed case study of how these ideas may be applied to understand the dynamical and spatiotemporal structure of Newtonian mechanics - in particular, in light of the symmetries of Newtonian theory. In so doing, it brings together a great deal of exciting recent work in the literature, and is sure to be a valuable companion for all those interested in these topics.
Download or read book Elementary Geometry from an Advanced Standpoint written by Edwin E. Moise and published by Addison Wesley. This book was released on 1990 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students can rely on Moise's clear and thorough presentation of basic geometry theorems. The author assumes that students have no previous knowledge of the subject and presents the basics of geometry from the ground up. This comprehensive approach gives instructors flexibility in teaching. For example, an advanced class may progress rapidly through Chapters 1-7 and devote most of its time to the material presented in Chapters 8, 10, 14, 19, and 20. Similarly, a less advanced class may go carefully through Chapters 1-7, and omit some of the more difficult chapters, such as 20 and 24.
Download or read book Synthetic Philosophy of Contemporary Mathematics written by Fernando Zalamea and published by National Geographic Books. This book was released on 2012-09-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest. A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest, this book gives the inquisitive non-specialist an insight into the conceptual transformations and intellectual orientations of modern and contemporary mathematics. The predominant analytic approach, with its focus on the formal, the elementary and the foundational, has effectively divorced philosophy from the real practice of mathematics and the profound conceptual shifts in the discipline over the last century. The first part discusses the specificity of modern (1830–1950) and contemporary (1950 to the present) mathematics, and reviews the failure of mainstream philosophy of mathematics to address this specificity. Building on the work of the few exceptional thinkers to have engaged with the “real mathematics” of their era (including Lautman, Deleuze, Badiou, de Lorenzo and Châtelet), Zalamea challenges philosophy's self-imposed ignorance of the “making of mathematics.” In the second part, thirteen detailed case studies examine the greatest creators in the field, mapping the central advances accomplished in mathematics over the last half-century, exploring in vivid detail the characteristic creative gestures of modern master Grothendieck and contemporary creators including Lawvere, Shelah, Connes, and Freyd. Drawing on these concrete examples, and oriented by a unique philosophical constellation (Peirce, Lautman, Merleau-Ponty), in the third part Zalamea sets out the program for a sophisticated new epistemology, one that will avail itself of the powerful conceptual instruments forged by the mathematical mind, but which have until now remained largely neglected by philosophers.
