Geometries and Transformations


Author: Norman W. Johnson

Publisher: Cambridge University Press

ISBN: 1107103401

Category: Mathematics

Page: 350

View: 7301

A readable exposition of how Euclidean and other geometries can be distinguished using linear algebra and transformation groups.

Euclidean Geometry and Transformations


Author: Clayton W. Dodge

Publisher: Courier Corporation

ISBN: 9780486434766

Category: Mathematics

Page: 295

View: 961

This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 edition.

College Geometry


Author: Howard Whitley Eves,Howard Eves

Publisher: Jones & Bartlett Learning

ISBN: 9780867204759

Category: Mathematics

Page: 370

View: 8738


Geometry of Möbius Transformations

Elliptic, Parabolic and Hyperbolic Actions of SL2[real Number]


Author: Vladimir V. Kisil

Publisher: World Scientific

ISBN: 1848168586

Category: Mathematics

Page: 192

View: 927

This book is a unique exposition of rich and inspiring geometries associated with Möbius transformations of the hypercomplex plane. The presentation is self-contained and based on the structural properties of the group SL2(R). Starting from elementary facts in group theory, the author unveils surprising new results about the geometry of circles, parabolas and hyperbolas, using an approach based on the Erlangen programme of F Klein, who defined geometry as a study of invariants under a transitive group action.The treatment of elliptic, parabolic and hyperbolic Möbius transformations is provided in a uniform way. This is possible due to an appropriate usage of complex, dual and double numbers which represent all non-isomorphic commutative associative two-dimensional algebras with unit. The hypercomplex numbers are in perfect correspondence with the three types of geometries concerned. Furthermore, connections with the physics of Minkowski and Galilean space-time are considered.

Transformation Geometry

An Introduction to Symmetry


Author: George E. Martin

Publisher: Springer Science & Business Media

ISBN: 9780387906362

Category: Mathematics

Page: 240

View: 7439

Transformation Geometry: An Introduction to Symmetry offers a modern approach to Euclidean Geometry. This study of the automorphism groups of the plane and space gives the classical concrete examples that serve as a meaningful preparation for the standard undergraduate course in abstract algebra. The detailed development of the isometries of the plane is based on only the most elementary geometry and is appropriate for graduate courses for secondary teachers.

A Course in Modern Geometries


Author: Judith N. Cederberg

Publisher: Springer Science & Business Media

ISBN: 1475734905

Category: Mathematics

Page: 441

View: 5961

Designed for a junior-senior level course for mathematics majors, including those who plan to teach in secondary school. The first chapter presents several finite geometries in an axiomatic framework, while Chapter 2 continues the synthetic approach in introducing both Euclids and ideas of non-Euclidean geometry. There follows a new introduction to symmetry and hands-on explorations of isometries that precedes an extensive analytic treatment of similarities and affinities. Chapter 4 presents plane projective geometry both synthetically and analytically, and the new Chapter 5 uses a descriptive and exploratory approach to introduce chaos theory and fractal geometry, stressing the self-similarity of fractals and their generation by transformations from Chapter 3. Throughout, each chapter includes a list of suggested resources for applications or related topics in areas such as art and history, plus this second edition points to Web locations of author-developed guides for dynamic software explorations of the Poincaré model, isometries, projectivities, conics and fractals. Parallel versions are available for "Cabri Geometry" and "Geometers Sketchpad".

Geometry of Complex Numbers


Author: Hans Schwerdtfeger

Publisher: Courier Corporation

ISBN: 0486135861

Category: Mathematics

Page: 224

View: 2940

Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries.

Bäcklund and Darboux Transformations

The Geometry of Solitons : AARMS-CRM Workshop, June 4-9, 1999, Halifax, N.S., Canada


Author: A. A. Coley

Publisher: American Mathematical Soc.

ISBN: 9780821870259

Category: Mathematics

Page: 436

View: 7539

This book is devoted to a classical topic that has undergone rapid and fruitful development over the past 25 years, namely Backlund and Darboux transformations and their applications in the theory of integrable systems, also known as soliton theory. The book consists of two parts. The first is a series of introductory pedagogical lectures presented by leading experts in the field. They are devoted respectively to Backlund transformations of Painleve equations, to the dressing methodand Backlund and Darboux transformations, and to the classical geometry of Backlund transformations and their applications to soliton theory. The second part contains original contributions that represent new developments in the theory and applications of these transformations. Both the introductorylectures and the original talks were presented at an International Workshop that took place in Halifax, Nova Scotia (Canada). This volume covers virtually all recent developments in the theory and applications of Backlund and Darboux transformations.

Digital Geometry

Geometric Methods for Digital Picture Analysis


Author: Reinhard Klette,Azriel Rosenfeld

Publisher: Elsevier

ISBN: 0080477267

Category: Computers

Page: 672

View: 921

Digital geometry is about deriving geometric information from digital pictures. The field emerged from its mathematical roots some forty-years ago through work in computer-based imaging, and it is used today in many fields, such as digital image processing and analysis (with applications in medical imaging, pattern recognition, and robotics) and of course computer graphics. Digital Geometry is the first book to detail the concepts, algorithms, and practices of the discipline. This comphrehensive text and reference provides an introduction to the mathematical foundations of digital geometry, some of which date back to ancient times, and also discusses the key processes involved, such as geometric algorithms as well as operations on pictures. *A comprehensive text and reference written by pioneers in digital geometry, image processing and analysis, and computer vision *Provides a collection of state-of-the-art algorithms for a wide variety of geometrical picture analysis tasks, including extracting data from digital images and making geometric measurements on the data *Includes exercises, examples, and references to related or more advanced work

Mathematics for Quantum Chemistry


Author: Jay Martin Anderson

Publisher: Courier Corporation

ISBN: 0486151484

Category: Science

Page: 160

View: 7643

Introduction to problems of molecular structure and motion covers calculus of orthogonal functions, algebra of vector spaces, and Lagrangian and Hamiltonian formulation of classical mechanics. Answers to problems. 1966 edition.

How to Solve Applied Mathematics Problems


Author: B. L. Moiseiwitsch

Publisher: Courier Corporation

ISBN: 0486285227

Category: Mathematics

Page: 336

View: 1944

This workbook bridges the gap between lectures and practical applications, offering students of mathematics, engineering, and physics the chance to practice solving problems from a wide variety of fields. 2011 edition.

Introduction to Crystallography


Author: Donald E. Sands

Publisher: Courier Corporation

ISBN: 0486136809

Category: Science

Page: 192

View: 871

Clear, concise explanation of logical development of basic crystallographic concepts. Topics include crystals and lattices, symmetry, x-ray diffraction, and more. Problems, with answers. 114 illustrations. 1969 edition.

Galois Theory

Lectures Delivered at the University of Notre Dame by Emil Artin (Notre Dame Mathematical Lectures,


Author: Emil Artin

Publisher: Courier Corporation

ISBN: 048615825X

Category: Mathematics

Page: 86

View: 3985

Clearly presented discussions of fields, vector spaces, homogeneous linear equations, extension fields, polynomials, algebraic elements, as well as sections on solvable groups, permutation groups, solution of equations by radicals, and other concepts. 1966 edition.

Transformation geometry


Author: Jagat Narain Kapur

Publisher: N.A


Category: Transformations (Mathematics)

Page: 257

View: 8424

From a Geometrical Point of View

A Study of the History and Philosophy of Category Theory


Author: Jean-Pierre Marquis

Publisher: Springer Science & Business Media

ISBN: 1402093845

Category: Science

Page: 310

View: 9307

From a Geometrical Point of View explores historical and philosophical aspects of category theory, trying therewith to expose its significance in the mathematical landscape. The main thesis is that Klein’s Erlangen program in geometry is in fact a particular instance of a general and broad phenomenon revealed by category theory. The volume starts with Eilenberg and Mac Lane’s work in the early 1940’s and follows the major developments of the theory from this perspective. Particular attention is paid to the philosophical elements involved in this development. The book ends with a presentation of categorical logic, some of its results and its significance in the foundations of mathematics. From a Geometrical Point of View aims to provide its readers with a conceptual perspective on category theory and categorical logic, in order to gain insight into their role and nature in contemporary mathematics. It should be of interest to mathematicians, logicians, philosophers of mathematics and science in general, historians of contemporary mathematics, physicists and computer scientists.

Geometric Transformations IV

Circular Transformations


Author: I. M. Yaglom

Publisher: MAA

ISBN: 9780883856482

Category: Mathematics

Page: 285

View: 2264

The familiar plane geometry of secondary school - figures composed of lines and circles - takes on a new life when viewed as the study of properties that are preserved by special groups of transformations. No longer is there a single, universal geometry: different sets of transformations of the plane correspond to intriguing, disparate geometries. This book is the concluding Part IV of Geometric Transformations, but it can be studied independently of Parts I, II, and III. The present Part IV develops the geometry of transformations of the plane that map circles to circles (conformal or anallagmatic geometry). The notion of inversion, or reflection in a circle, is the key tool employed. Applications include ruler-and-compass constructions and the Poincar model of hyperbolic geometry. The straightforward, direct presentation assumes only some background in elementary geometry and trigonometry.