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Author: I. M. Yaglom
Publisher: MAA
ISBN: 9780883856482
Category : Mathematics
Languages : en
Pages : 302
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Book Description
A comprehensive treatment of the geometry of circular transformations.
Author: I. M. Yaglom
Publisher: MAA
ISBN: 9780883856482
Category : Mathematics
Languages : en
Pages : 302
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Book Description
A comprehensive treatment of the geometry of circular transformations.
Author: Isaak Moiseevich I︠A︡glom
Publisher:
ISBN:
Category : Transformations (Mathematics)
Languages : en
Pages : 206
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Book Description
Author: Issak Moiseevich Yaglom
Publisher:
ISBN: 9780883856000
Category :
Languages : en
Pages :
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Book Description
Author: Isaak Moiseevich I︠A︡glom
Publisher:
ISBN: 9780883856000
Category : Geometry
Languages : en
Pages :
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Book Description
Author: P. S. Modenov
Publisher: Academic Press
ISBN: 1483261484
Category : Mathematics
Languages : en
Pages : 171
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Book Description
Geometric Transformations, Volume 1: Euclidean and Affine Transformations focuses on the study of coordinates, trigonometry, transformations, and linear equations. The publication first takes a look at orthogonal transformations, including orthogonal transformations of the first and second kinds; representations of orthogonal transformations as the products of fundamental orthogonal transformations; and representation of an orthogonal transformation of space as a product of fundamental orthogonal transformations. The text then examines similarity and affine transformations. Topics include properties of affine mappings, Darboux's lemma and its consequences, affine transformations in coordinates, homothetic transformations, similarity transformations of the plane in coordinates, and similarity mapping. The book takes a look at the representation of a similarity transformation as the product of a homothetic transformation and an orthogonal transformation; application of affine transformations to the investigation of properties of the ellipse; and representation of any affine transformation as a product of affine transformations of the simplest types. The manuscript is a valuable reference for high school teachers and readers interested in the Euclidean and affine transformations.
Author:
Publisher: Academic Press
ISBN: 0080873596
Category : Mathematics
Languages : en
Pages : 477
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Book Description
Introduction to Compact Transformation Groups
Author: Shoshichi Kobayashi
Publisher: Springer Science & Business Media
ISBN: 3642619819
Category : Mathematics
Languages : en
Pages : 192
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Book Description
Given a mathematical structure, one of the basic associated mathematical objects is its automorphism group. The object of this book is to give a biased account of automorphism groups of differential geometric struc tures. All geometric structures are not created equal; some are creations of ~ods while others are products of lesser human minds. Amongst the former, Riemannian and complex structures stand out for their beauty and wealth. A major portion of this book is therefore devoted to these two structures. Chapter I describes a general theory of automorphisms of geometric structures with emphasis on the question of when the automorphism group can be given a Lie group structure. Basic theorems in this regard are presented in §§ 3, 4 and 5. The concept of G-structure or that of pseudo-group structure enables us to treat most of the interesting geo metric structures in a unified manner. In § 8, we sketch the relationship between the two concepts. Chapter I is so arranged that the reader who is primarily interested in Riemannian, complex, conformal and projective structures can skip §§ 5, 6, 7 and 8. This chapter is partly based on lec tures I gave in Tokyo and Berkeley in 1965.
Author: Stephen L. Campbell
Publisher: SIAM
ISBN: 0898716713
Category : Mathematics
Languages : en
Pages : 288
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Book Description
Provides comprehensive coverage of the mathematical theory of generalized inverses and a wide range of important and practical applications.
Author: Ronald N. Umble
Publisher: CRC Press
ISBN: 1482234718
Category : Mathematics
Languages : en
Pages : 239
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Book Description
Designed for a one-semester course at the junior undergraduate level, Transformational Plane Geometry takes a hands-on, interactive approach to teaching plane geometry. The book is self-contained, defining basic concepts from linear and abstract algebra gradually as needed. The text adheres to the National Council of Teachers of Mathematics Principles and Standards for School Mathematics and the Common Core State Standards Initiative Standards for Mathematical Practice. Future teachers will acquire the skills needed to effectively apply these standards in their classrooms. Following Felix Klein’s Erlangen Program, the book provides students in pure mathematics and students in teacher training programs with a concrete visual alternative to Euclid’s purely axiomatic approach to plane geometry. It enables geometrical visualization in three ways: Key concepts are motivated with exploratory activities using software specifically designed for performing geometrical constructions, such as Geometer’s Sketchpad. Each concept is introduced synthetically (without coordinates) and analytically (with coordinates). Exercises include numerous geometric constructions that use a reflecting instrument, such as a MIRA. After reviewing the essential principles of classical Euclidean geometry, the book covers general transformations of the plane with particular attention to translations, rotations, reflections, stretches, and their compositions. The authors apply these transformations to study congruence, similarity, and symmetry of plane figures and to classify the isometries and similarities of the plane.
Author: Alexandru Scorpan
Publisher: American Mathematical Society
ISBN: 1470468611
Category : Mathematics
Languages : en
Pages : 614
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Book Description
What a wonderful book! I strongly recommend this book to anyone, especially graduate students, interested in getting a sense of 4-manifolds. —MAA Reviews The book gives an excellent overview of 4-manifolds, with many figures and historical notes. Graduate students, nonexperts, and experts alike will enjoy browsing through it. — Robion C. Kirby, University of California, Berkeley This book offers a panorama of the topology of simply connected smooth manifolds of dimension four. Dimension four is unlike any other dimension; it is large enough to have room for wild things to happen, but small enough so that there is no room to undo the wildness. For example, only manifolds of dimension four can exhibit infinitely many distinct smooth structures. Indeed, their topology remains the least understood today. To put things in context, the book starts with a survey of higher dimensions and of topological 4-manifolds. In the second part, the main invariant of a 4-manifold—the intersection form—and its interaction with the topology of the manifold are investigated. In the third part, as an important source of examples, complex surfaces are reviewed. In the final fourth part of the book, gauge theory is presented; this differential-geometric method has brought to light how unwieldy smooth 4-manifolds truly are, and while bringing new insights, has raised more questions than answers. The structure of the book is modular, organized into a main track of about two hundred pages, augmented by extensive notes at the end of each chapter, where many extra details, proofs and developments are presented. To help the reader, the text is peppered with over 250 illustrations and has an extensive index.
