Dr. Math Introduces Geometry  Pdf Download eBook
Read or Download Pdf Dr. Math Introduces Geometry by The Math Forum full pdf 192 pages, read more Juvenile Nonfiction books related to Dr. Math Introduces GeometryDr. Math Introduces Geometry
By The Math Forum Format : Pdf, ePub, Mobi, Kindle
 Publisher : John Wiley & Sons
 Isbn : 9780471677543
 Pages : 192
 Category : Juvenile Nonfiction
 Reads : 206
 File Pdf: drmathintroducesgeometry.pdf
Book Summary:
You, Too, Can Understand Geometry  Just Ask Dr. Math! Have you started studying geometry in math class? Do you get totally lost trying to find the perimeter of a rectangle or the circumference of a circle? Don't worry. Grasping the basics of geometry doesn't have to be as scary as it sounds. Dr. Maththe popular online math resourceis here to help! Students just like you have been turning to Dr. Math for years asking questions about math problems, and the math doctors at The Math Forum have helped them find the answers with lots of clear explanations and helpful hints. Now, with Dr. Math Introduces Geometry, you'll learn just what it takes to succeed in this subject. You'll find the answers to dozens of real questions from students who needed help understanding the basic concepts of geometry, from lines, rays, and angles to measuring threedimensional objects and applying geometry in the real world. Pretty soon, everything from recognizing types of quadrilaterals to finding surface area to counting lines of symmetry will make sense. Plus, you'll get plenty of tips for working with tricky problems submitted by other kids who are just as confused as you are. You won't find a better introduction to the world and language of geometry anywhere!
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 File Pdf: geometryii.pdf
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 Isbn : 9789814479592
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 File Pdf: analytichyperbolicgeometry.pdf
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' This is the first book on analytic hyperbolic geometry, fully analogous to analytic Euclidean geometry. Analytic hyperbolic geometry regulates relativistic mechanics just as analytic Euclidean geometry regulates classical mechanics. The book presents a novel gyrovector space approach to analytic hyperbolic geometry, fully analogous to the wellknown vector space approach to Euclidean geometry. A gyrovector is a hyperbolic vector. Gyrovectors are equivalence classes of directed gyrosegments that add according to the gyroparallelogram law just as vectors are equivalence classes of directed segments that add according to the parallelogram law. In the resulting “gyrolanguage” of the book one attaches the prefix “gyro” to a classical term to mean the analogous term in hyperbolic geometry. The prefix stems from Thomas gyration, which is the mathematical abstraction of the relativistic effect known as Thomas precession. 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Gyrogroups, both gyrocommutative and nongyrocommutative, abound in group theory. Surprisingly, the seemingly structureless Einstein velocity addition of special relativity turns out to be a gyrocommutative gyrogroup operation. Introducing scalar multiplication, some gyrocommutative gyrogroups of gyrovectors become gyrovector spaces. The latter, in turn, form the setting for analytic hyperbolic geometry just as vector spaces form the setting for analytic Euclidean geometry. By hybrid techniques of differential geometry and gyrovector spaces, it is shown that Einstein (Möbius) gyrovector spaces form the setting for BeltramiKlein (Poincaré) ball models of hyperbolic geometry. Finally, novel applications of Möbius gyrovector spaces in quantum computation, and of Einstein gyrovector spaces in special relativity, are presented. Contents: GyrogroupsGyrocommutative GyrogroupsGyrogroup ExtensionGyrovectors and CogyrovectorsGyrovector SpacesRudiments of Differential GeometryGyrotrigonometryBloch Gyrovector of Quantum ComputationSpecial Theory of Relativity: The Analytic Hyperbolic Geometric Viewpoint Readership: Undergraduates, graduate students, researchers and academics in geometry, algebra, mathematical physics, theoretical physics and astronomy. Keywords:Analytic Hyperbolic Geometry;Gyrogroup;Gyrovector Space;Hyperbolic Geometry;Relativistic Mass;Special RelativityKey Features:Develops an elegant conversion formula from the hyperbolic triangle hyperbolic angles to its hyperbolic side lengthsIntroduces hyperbolic vectors, called “gyrovectors", and demonstrates that Einstein velocity addition is nothing but a gyrovector addition in a gyrovector space just as Newton velocity addition is a vector addition in a vector spaceShows that Einstein's relativistic mass meshes extraordinarily well with analytic hyperbolic geometry, where it captures remarkable analogies with Newton's classical mass and the analytic Euclidean geometry of the center of momentumReviews:“This new book by Ungar is very wellwritten, with plenty of references and explanatory pictures. Almost all chapters include exercises which ensure that the book will reach a large audience from undergraduate and graduate students to researchers and academics in different areas of mathematics and mathematical physics. In this book, the author sets out his improved gyrotheory, capturing the curiosity of the reader with discernment, elegance and simplicity.”Mathematical Reviews “This book under review provides an efficient algebraic formalism for studying the hyperbolic geometry of Bolyai and Lobachevsky, which underlies Einstein special relativity … It is of interest both to mathematicians, working in the field of geometry, and the physicists specialized in relativity or quantum computation theory … It is recommended to graduate students and researchers interested in the interrelations among nonassociative algebra, hyperbolic and differential geometry, Einstein relativity theory and the quantum computation theory.”Journal of Geometry and Symmetry in Physics “This book represents an exposition of the author's singlehanded creation, over the past 17 years, of an algebraic language in which both hyperbolic geometry and special relativity find an aesthetically pleasing formulation, very much like Euclidean geometry and Newtonian mechanics find them in the language of vector spaces.”Zentralblatt MATH '
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 Publisher : Springer Science & Business Media
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 File Pdf: geometricanalysisandapplicationstoquantumfieldtheory.pdf
Book Summary:
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 Publisher : Springer Science & Business Media
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 File Pdf: firststepsindifferentialgeometry.pdf
Book Summary:
Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as "the study of structures on the tangent space," and this text develops this point of view. This book, unlike other introductory texts in differential geometry, develops the architecture necessary to introduce symplectic and contact geometry alongside its Riemannian cousin. The main goal of this book is to bring the undergraduate student who already has a solid foundation in the standard mathematics curriculum into contact with the beauty of higher mathematics. In particular, the presentation here emphasizes the consequences of a definition and the careful use of examples and constructions in order to explore those consequences.
Algebra & Geometry
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 Publisher : CRC Press
 Isbn : 9781000402506
 Pages : 424
 Category : Mathematics
 Reads : 141
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Algebra & Geometry: An Introduction to University Mathematics, Second Edition provides a bridge between high school and undergraduate mathematics courses on algebra and geometry. The author shows students how mathematics is more than a collection of methods by presenting important ideas and their historical origins throughout the text. He incorporates a handson approach to proofs and connects algebra and geometry to various applications. The text focuses on linear equations, polynomial equations, and quadratic forms. The first few chapters cover foundational topics, including the importance of proofs and a discussion of the properties commonly encountered when studying algebra. The remaining chapters form the mathematical core of the book. These chapters explain the solutions of different kinds of algebraic equations, the nature of the solutions, and the interplay between geometry and algebra. New to the second edition Several updated chapters, plus an allnew chapter discussing the construction of the real numbers by means of approximations by rational numbers Includes fifteen short ‘essays’ that are accessible to undergraduate readers, but which direct interested students to more advanced developments of the material Expanded references Contains chapter exercises with solutions provided online at www.routledge.com/9780367563035
The Geometry of Discrete Groups
By Alan F. Beardon Format : Pdf, ePub, Mobi, Kindle
 Publisher : Springer Science & Business Media
 Isbn : 9781461211464
 Pages : 340
 Category : Mathematics
 Reads : 461
 File Pdf: thegeometryofdiscretegroups.pdf
Book Summary:
This text is intended to serve as an introduction to the geometry of the action of discrete groups of Mobius transformations. The subject matter has now been studied with changing points of emphasis for over a hundred years, the most recent developments being connected with the theory of 3manifolds: see, for example, the papers of Poincare [77] and Thurston [101]. About 1940, the now wellknown (but virtually unobtainable) FenchelNielsen manuscript appeared. Sadly, the manuscript never appeared in print, and this more modest text attempts to display at least some of the beautiful geo metrical ideas to be found in that manuscript, as well as some more recent material. The text has been written with the conviction that geometrical explana tions are essential for a full understanding of the material and that however simple a matrix proof might seem, a geometric proof is almost certainly more profitable. Further, wherever possible, results should be stated in a form that is invariant under conjugation, thus making the intrinsic nature of the result more apparent. Despite the fact that the subject matter is concerned with groups of isometries of hyperbolic geometry, many publications rely on Euclidean estimates and geometry. However, the recent developments have again emphasized the need for hyperbolic geometry, and I have included a comprehensive chapter on analytical (not axiomatic) hyperbolic geometry. It is hoped that this chapter will serve as a "dictionary" offormulae in plane hyperbolic geometry and as such will be of interest and use in its own right.
Combinatorial Geometry and Its Algorithmic Applications
By János Pach,Micha Sharir,Mîkā Šārîr Format : Pdf, ePub, Mobi, Kindle
 Publisher : American Mathematical Soc.
 Isbn : 9780821846919
 Pages : 235
 Category : Mathematics
 Reads : 992
 File Pdf: combinatorialgeometryanditsalgorithmicapplications.pdf
Book Summary:
This book, based on the authors' lecture series at a 2006 satellite meeting of the International Congress of Mathematicians, offers a comprehensive survey of core areas of combinatorial geometry. These lecture notes aptly describe both the history and the state of the art of these topics. These combinatorial techniques have found applications in areas of computer science ranging from graph drawing to frequency allocation in cellular networks.
Riemannian Geometry and Geometric Analysis
By Jürgen Jost Format : Pdf, ePub, Mobi, Kindle
 Publisher : Springer Science & Business Media
 Isbn : 9783662223857
 Pages : 458
 Category : Mathematics
 Reads : 566
 File Pdf: riemanniangeometryandgeometricanalysis.pdf
Book Summary:
FROM REVIEWS OF THE FIRST EDITION "a very readable introduction to Riemannian geometry...it is most welcome...The book is made more interesting by the perspectives in various sections, where the author mentions the history and development of the material and provides the reader with references."MATHEMATICAL REVIEWS
Rings and Geometry
By R. Kaya,P. Plaumann,K. Strambach Format : Pdf, ePub, Mobi, Kindle
 Publisher : Springer Science & Business Media
 Isbn : 9789400954601
 Pages : 568
 Category : Mathematics
 Reads : 566
 File Pdf: ringsandgeometry.pdf
Book Summary:
When looking for applications of ring theory in geometry, one first thinks of algebraic geometry, which sometimes may even be interpreted as the concrete side of commutative algebra. However, this highly de veloped branch of mathematics has been dealt with in a variety of mono graphs, so that  in spite of its technical complexity  it can be regarded as relatively well accessible. While in the last 120 years algebraic geometry has again and again attracted concentrated interes which right now has reached a peak once more  , the numerous other applications of ring theory in geometry have not been assembled in a textbook and are scattered in many papers throughout the literature, which makes it hard for them to emerge from the shadow of the brilliant theory of algebraic geometry. It is the aim of these proceedings to give a unifying presentation of those geometrical applications of ring theo~y outside of algebraic geometry, and to show that they offer a considerable wealth of beauti ful ideas, too. Furthermore it becomes apparent that there are natural connections to many branches of modern mathematics, e. g. to the theory of (algebraic) groups and of Jordan algebras, and to combinatorics. To make these remarks more precise, we will now give a description of the contents. In the first chapter, an approach towards a theory of noncommutative algebraic geometry is attempted from two different points of view.
Spherical Geometry and Its Applications
By Marshall A. Whittlesey Format : Pdf, ePub, Mobi, Kindle
 Publisher : CRC Press
 Isbn : 9781000617542
 Pages : 335
 Category : Mathematics
 Reads : 588
 File Pdf: sphericalgeometryanditsapplications.pdf
Book Summary:
Spherical Geometry and Its Applications introduces spherical geometry and its practical applications in a mathematically rigorous form. The text can serve as a course in spherical geometry for mathematics majors. Readers from various academic backgrounds can comprehend various approaches to the subject. The book introduces an axiomatic system for spherical geometry and uses it to prove the main theorems of the subject. It also provides an alternate approach using quaternions. The author illustrates how a traditional axiomatic system for plane geometry can be modified to produce a different geometric world – but a geometric world that is no less real than the geometric world of the plane. Features: A wellrounded introduction to spherical geometry Provides several proofs of some theorems to appeal to larger audiences Presents principal applications: the study of the surface of the earth, the study of stars and planets in the sky, the study of three and fourdimensional polyhedra, mappings of the sphere, and crystallography Many problems are based on propositions from the ancient text Sphaerica of Menelaus
Invariant Methods in Discrete and Computational Geometry
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 Category : Computers
 Reads : 391
 File Pdf: invariantmethodsindiscreteandcomputationalgeometry.pdf
Book Summary:
Invariant, or coordinatefree methods provide a natural framework for many geometric questions. Invariant Methods in Discrete and Computational Geometry provides a basic introduction to several aspects of invariant theory, including the supersymmetric algebra, the GrassmannCayler algebra, and Chow forms. It also presents a number of current research papers on invariant theory and its applications to problems in geometry, such as automated theorem proving and computer vision. Audience: Researchers studying mathematics, computers and robotics.
PythagoreanHodograph Curves: Algebra and Geometry Inseparable
By Rida T Farouki Format : Pdf, ePub, Mobi, Kindle
 Publisher : Springer Science & Business Media
 Isbn : 9783540733980
 Pages : 728
 Category : Mathematics
 Reads : 753
 File Pdf: pythagoreanhodographcurves.pdf
Book Summary:
By virtue of their special algebraic structures, Pythagoreanhodograph (PH) curves offer unique advantages for computeraided design and manufacturing, robotics, motion control, path planning, computer graphics, animation, and related fields. This book offers a comprehensive and selfcontained treatment of the mathematical theory of PH curves, including algorithms for their construction and examples of their practical applications. It emphasizes the interplay of ideas from algebra and geometry and their historical origins and includes many figures, worked examples, and detailed algorithm descriptions.
Noncommutative Geometry and Particle Physics
By Walter D. van Suijlekom Format : Pdf, ePub, Mobi, Kindle
 Publisher : Springer
 Isbn : 9789401791625
 Pages : 237
 Category : Science
 Reads : 978
 File Pdf: noncommutativegeometryandparticlephysics.pdf
Book Summary:
This book provides an introduction to noncommutative geometry and presents a number of its recent applications to particle physics. It is intended for graduate students in mathematics/theoretical physics who are new to the field of noncommutative geometry, as well as for researchers in mathematics/theoretical physics with an interest in the physical applications of noncommutative geometry. 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 nonabelian YangMills 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.
Perspectives on the Teaching of Geometry for the 21st Century
By C. Mammana,V. Villani Format : Pdf, ePub, Mobi, Kindle
 Publisher : Springer Science & Business Media
 Isbn : 9789401152266
 Pages : 353
 Category : Education
 Reads : 739
 File Pdf: perspectivesontheteachingofgeometryforthe21stcentury.pdf
Book Summary:
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.
Riemannian Geometry and Geometric Analysis
By Jürgen Jost Format : Pdf, ePub, Mobi, Kindle
 Publisher : Springer Science & Business Media
 Isbn : 9783540288916
 Pages : 566
 Category : Mathematics
 Reads : 519
 File Pdf: riemanniangeometryandgeometricanalysis.pdf
Book Summary:
Offering some of the topics of contemporary mathematical research, this fourth edition includes a systematic introduction to Kahler geometry and the presentation of additional techniques from geometric analysis.
The Geometric Vein
By C. Davis,B. Grünbaum,F.A. Sherk Format : Pdf, ePub, Mobi, Kindle
 Publisher : Springer Science & Business Media
 Isbn : 9781461256489
 Pages : 598
 Category : Mathematics
 Reads : 261
 File Pdf: thegeometricvein.pdf
Book Summary:
Geometry has been defined as that part of mathematics which makes appeal to the sense of sight; but this definition is thrown in doubt by the existence of great geometers who were blind or nearly so, such as Leonhard Euler. Sometimes it seems that geometric methods in analysis, socalled, consist in having recourse to notions outside those apparently relevant, so that geometry must be the joining of unlike strands; but then what shall we say of the importance of axiomatic programmes in geometry, where reference to notions outside a restricted reper tory is banned? Whatever its definition, geometry clearly has been more than the sum of its results, more than the consequences of some few axiom sets. It has been a major current in mathematics, with a distinctive approach and a distinc ti v e spirit. A current, furthermore, which has not been constant. In the 1930s, after a period of pervasive prominence, it appeared to be in decline, even passe. These same years were those in which H. S. M. Coxeter was beginning his scientific work. Undeterred by the unfashionability of geometry, Coxeter pursued it with devotion and inspiration. By the 1950s he appeared to the broader mathematical world as a consummate practitioner of a peculiar, outoftheway art. Today there is no longer anything that outoftheway about it. Coxeter has contributed to, exemplified, we could almost say presided over an unanticipated and dra matic revival of geometry.
Surveys on Discrete and Computational Geometry
By Jacob E. Goodman Format : Pdf, ePub, Mobi, Kindle
 Publisher : American Mathematical Soc.
 Isbn : 9780821842393
 Pages : 556
 Category : Mathematics
 Reads : 671
 File Pdf: surveysondiscreteandcomputationalgeometry.pdf
Book Summary:
This volume contains nineteen survey papers describing the state of current research in discrete and computational geometry as well as a set of open problems presented at the 2006 AMSIMSSIAM Summer Research Conference Discrete and Computational GeometryTwenty Years Later, held in Snowbird, Utah, in June 2006. Topics surveyed include metric graph theory, lattice polytopes, the combinatorial complexity of unions of geometric objects, line and pseudoline arrangements, algorithmic semialgebraic geometry, persistent homology, unfolding polyhedra, pseudotriangulations, nonlinear computational geometry, $k$sets, and the computational complexity of convex bodies.
Math for Real Life
By Jim Libby Format : Pdf, ePub, Mobi, Kindle
 Publisher : McFarland
 Isbn : 9781476626758
 Pages : 212
 Category : Education
 Reads : 848
 File Pdf: mathforreallife.pdf
Book Summary:
“Where are we ever going to use this?” Every high school math student has asked this question. Often teachers themselves aren’t sure how to respond. One answer is that higher mathematics learned in high school will be essential to learning yet more at the college level. A more satisfactory answer calls for an awareness of how math is applied in many specific areas. Written primarily for teachers, this book presents hundreds of practical applications for mathematics—from baseball statistics to the theory of relativity—that can be understood by anyone with a knowledge of high school algebra, geometry and trigonometry.