A Course in Modern Geometries

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Author: Judith N. Cederberg

Publisher: Springer Science & Business Media

ISBN: 1475734905

Category: Mathematics

Page: 441

View: 6348

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".

Modern Geometries

Non-Euclidean, Projective, and Discrete

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Author: Michael Henle

Publisher: Pearson College Division

ISBN: 9780130323132

Category: Mathematics

Page: 389

View: 6673

Engaging, accessible, and extensively illustrated, this brief, but solid introduction to modern geometry describes geometry as it is understood and used by contemporary mathematicians and theoretical scientists. Basically non-Euclidean in approach, it relates geometry to familiar ideas from analytic geometry, staying firmly in the Cartesian plane. It uses the principle geometric concept of congruence or geometric transformation--introducing and using the Erlanger Program explicitly throughout. It features significant modern applications of geometry--e.g., the geometry of relativity, symmetry, art and crystallography, finite geometry and computation. Covers a full range of topics from plane geometry, projective geometry, solid geometry, discrete geometry, and axiom systems. For anyone interested in an introduction to geometry used by contemporary mathematicians and theoretical scientists.

A Survey of Classical and Modern Geometries

With Computer Activities

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Author: Arthur Baragar

Publisher: Pearson College Division

ISBN: N.A

Category: Mathematics

Page: 370

View: 8249

This book emphasizes the beauty of geometry using a modern approach. Models & computer exercises help readers to cultivate geometric intuition. Topics include Euclidean Geometry, Hand Constructions, Geometer's Sketch Pad, Hyperbolic Geometry, Tilings & Lattices, Spherical Geometry, Projective Geometry, Finite Geometry, and Modern Geometry Research. Ideal for geometry at an intermediate level.

Modern Geometry— Methods and Applications

Part II: The Geometry and Topology of Manifolds

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Author: B.A. Dubrovin,A.T. Fomenko,S.P. Novikov

Publisher: Springer Science & Business Media

ISBN: 9780387961620

Category: Mathematics

Page: 432

View: 1391

Up until recently, Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education. The standard courses in the classical differential geometry of curves and surfaces which were given instead (and still are given in some places) have come gradually to be viewed as anachronisms. However, there has been hitherto no unanimous agreement as to exactly how such courses should be brought up to date, that is to say, which parts of modern geometry should be regarded as absolutely essential to a modern mathematical education, and what might be the appropriate level of abstractness of their exposition. The task of designing a modernized course in geometry was begun in 1971 in the mechanics division of the Faculty of Mechanics and Mathematics of Moscow State University. The subject-matter and level of abstractness of its exposition were dictated by the view that, in addition to the geometry of curves and surfaces, the following topics are certainly useful in the various areas of application of mathematics (especially in elasticity and relativity, to name but two), and are therefore essential: the theory of tensors (including covariant differentiation of them); Riemannian curvature; geodesics and the calculus of variations (including the conservation laws and Hamiltonian formalism); the particular case of skew-symmetric tensors (i. e.

Modern Geometry with Applications

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Author: George A. Jennings

Publisher: Springer Science & Business Media

ISBN: 1461208556

Category: Mathematics

Page: 204

View: 6854

This introduction to modern geometry differs from other books in the field due to its emphasis on applications and its discussion of special relativity as a major example of a non-Euclidean geometry. Additionally, it covers the two important areas of non-Euclidean geometry, spherical geometry and projective geometry, as well as emphasising transformations, and conics and planetary orbits. Much emphasis is placed on applications throughout the book, which motivate the topics, and many additional applications are given in the exercises. It makes an excellent introduction for those who need to know how geometry is used in addition to its formal theory.

An Essay on the Foundations of Modern Geometry

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Author: Bertrand Russell

Publisher: Courier Corporation

ISBN: 9780486495552

Category: Mathematics

Page: 224

View: 317

The author, a Nobel Laureate and one of the 20th century's most important logicians, asks and answers basic questions about the intersection of philosophy and higher mathematics. 1897 edition.

Modern Geometry

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Author: David A. Thomas

Publisher: Brooks/Cole Publishing Company

ISBN: 9780534365509

Category: Mathematics

Page: 348

View: 3163

MODERN GEOMETRY was written to provide undergraduate and graduate level mathematics education students with an introduction to both Euclidean and non-Euclidean geometries, appropriate to their needs as future junior and senior high school mathematics teachers. MODERN GEOMETRY provides a systematic survey of Euclidean, hyperbolic, transformation, fractal, and projective geometries. This approach is consistent with the recommendations of the National Council of Teachers of Mathematics (NCTM), the International Society for Technology in Education (ISTE), and other professional organizations active in the preparation and continuing professional development of K-12 mathematics teachers.

Mechanical Theorem Proving in Geometries

Basic Principles

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Author: Wen-tsün Wu

Publisher: Springer Science & Business Media

ISBN: 9783211825068

Category: Computers

Page: 288

View: 3711

This book is a translation of Professor Wu's seminal Chinese book of 1984 on Automated Geometric Theorem Proving. The translation was done by his former student Dongming Wang jointly with Xiaofan Jin so that authenticity is guaranteed. Meanwhile, automated geometric theorem proving based on Wu's method of characteristic sets has become one of the fundamental, practically successful, methods in this area that has drastically enhanced the scope of what is computationally tractable in automated theorem proving. This book is a source book for students and researchers who want to study both the intuitive first ideas behind the method and the formal details together with many examples.

College Geometry

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Author: Howard Whitley Eves,Howard Eves

Publisher: Jones & Bartlett Learning

ISBN: 9780867204759

Category: Mathematics

Page: 370

View: 1503

Mathematics

Modern Geometry

An Elementary Treatise on the Geometry of the Triangle and the Circle

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Author: Roger Arthur Johnson

Publisher: N.A

ISBN: N.A

Category: Geometry, Modern

Page: 319

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Journey Into Geometries

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Author: Marta Sved

Publisher: Cambridge University Press

ISBN: 9780883855003

Category: Mathematics

Page: 182

View: 8920

Informal introduction into the non-Euclidean geometries through a series of dialogues involving Alice in Wonderland.

Modern Geometry: Its Structure and Function

Teacher's Manual

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Author: Kenneth B. Henderson,Robert E. Pingry,George Albert Robinson

Publisher: N.A

ISBN: N.A

Category: Geometry

Page: 561

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Foundations of Incidence Geometry

Projective and Polar Spaces

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Author: Johannes Ueberberg

Publisher: Springer Science & Business Media

ISBN: 3642209726

Category: Mathematics

Page: 248

View: 1498

Incidence geometry is a central part of modern mathematics that has an impressive tradition. The main topics of incidence geometry are projective and affine geometry and, in more recent times, the theory of buildings and polar spaces. Embedded into the modern view of diagram geometry, projective and affine geometry including the fundamental theorems, polar geometry including the Theorem of Buekenhout-Shult and the classification of quadratic sets are presented in this volume. Incidence geometry is developed along the lines of the fascinating work of Jacques Tits and Francis Buekenhout. The book is a clear and comprehensible introduction into a wonderful piece of mathematics. More than 200 figures make even complicated proofs accessible to the reader.

Classical Geometries in Modern Contexts

Geometry of Real Inner Product Spaces

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Author: Walter Benz

Publisher: Springer Science & Business Media

ISBN: 9783764385415

Category: Mathematics

Page: 277

View: 4454

This book is based on real inner product spaces X of arbitrary (finite or infinite) dimension greater than or equal to 2. Designed as a two term graduate course, the book helps students to understand great ideas of classical geometries in a modern and general context. A real benefit is the dimension-free approach to important geometrical theories. The only prerequisites are basic linear algebra and basic 2- and 3-dimensional real geometry.