Transformation Geometry
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Transformation Groups In Differential Geometry
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Author : Shoshichi Kobayashi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Transformation Groups In Differential Geometry written by Shoshichi Kobayashi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Geometric Transformations
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Author : Răzvan Gelca
language : en
Publisher: Springer Nature
Release Date : 2022-02-16
Geometric Transformations written by Răzvan Gelca and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-16 with Mathematics categories.
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.
Transformation Geometry
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Author : George E. Martin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Transformation Geometry written by George E. Martin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Transformation Geometry
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Author : Max Jager
language : en
Publisher:
Release Date : 1969
Transformation Geometry written by Max Jager and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Transformations (Mathematics) categories.
Transformation Geometry
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Author : Max Jeger
language : en
Publisher:
Release Date : 1964
Transformation Geometry written by Max Jeger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Geometry categories.
Euclidean Geometry And Transformations
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Author : Clayton W. Dodge
language : en
Publisher: Courier Corporation
Release Date : 2012-04-26
Euclidean Geometry And Transformations written by Clayton W. Dodge and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-26 with Mathematics categories.
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.
Geometric Transformations For 3d Modeling
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Author : Michael E. Mortenson
language : en
Publisher:
Release Date : 2007
Geometric Transformations For 3d Modeling written by Michael E. Mortenson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Computers categories.
Written from a mathematical standpoint accessible to students, teachers, and professionals studying or practicing in engineering, mathematics, or physics, the new second edition is a comprehensive introduction to the theory and application of transformations. Presenting the more abstract foundation material in the first three chapters, Geometric Transformations in 3D Modeling reduces the clutter of theoretical derivation and development in the remainder of the text and introduces the operational and more application-oriented tools and concepts as the need arises. It assumes the reader has already taken analytic geometry and first-year calculus and has a working knowledge of basic matrix and vector algebra. This self-contained resource is sure to appeal to those working in 3D modeling, geometric modeling, computer graphics, animation, robotics, and kinematics. Explores and develops the subject in much greater breadth and depth than other books, offering readers a better understanding of transformation theory, the role of invariants, the uses of various notation systems, and the relations between transformations. Describes how geometric objects may change position, orientation, or even shape when subjected to mathematical operations, while properties characterizing their geometric identity and integrity remain unchanged. Presents eigenvalues, eigenvectors, and tensors in a way that makes it easier for readers to understand. Contains revised and improved figures, with many in color to highlight important features. Provides exercises throughout nearly all of the chapters whose answers are found at the end of the book.
Geometry Of Complex Numbers
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Author : Hans Schwerdtfeger
language : en
Publisher: Courier Corporation
Release Date : 2012-05-23
Geometry Of Complex Numbers written by Hans Schwerdtfeger and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-23 with Mathematics categories.
Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries.
Geometric Transformations Projective Transformations
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Author : Petr Sergeevich Modenov
language : en
Publisher:
Release Date : 1966
Geometric Transformations Projective Transformations written by Petr Sergeevich Modenov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Geometry, Algebraic categories.
Geometry Of Mobius Transformations Elliptic Parabolic And Hyperbolic Actions Of Sl2 R With Dvd Rom
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Author : Vladimir V Kisil
language : en
Publisher: World Scientific
Release Date : 2012-06-19
Geometry Of Mobius Transformations Elliptic Parabolic And Hyperbolic Actions Of Sl2 R With Dvd Rom written by Vladimir V Kisil and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-19 with Mathematics categories.
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./a
