Geometric Transformations
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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.
Geometric Transformations
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Author : Isaac Moisevitch Yaglom
language : en
Publisher:
Release Date : 1962
Geometric Transformations written by Isaac Moisevitch Yaglom and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with categories.
Geometric Transformations Iv
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Author : I. M. Yaglom
language : en
Publisher: MAA
Release Date : 2009-10-15
Geometric Transformations Iv written by I. M. Yaglom and has been published by MAA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-15 with Mathematics categories.
A comprehensive treatment of the geometry of circular transformations.
Projective Transformations
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Author : P. S. Modenov
language : en
Publisher: Academic Press
Release Date : 2014-05-12
Projective Transformations written by P. S. Modenov and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.
Geometric Transformations, Volume 2: Projective Transformations focuses on collinearity-preserving transformations of the projective plane. The book first offers information on projective transformations, as well as the concept of a projective plane, definition of a projective mapping, fundamental theorems on projective transformations, cross ratio, and harmonic sets. Examples of projective transformations, projective transformations in coordinates, quadratic curves in the projective plane, and projective transformations of space are also discussed. The text then examines inversion, including the power of a point with respect to a circle, definition and properties of inversion, and circle transformations and the fundamental theorem. The manuscript elaborates on the principle of duality. The manuscript is designed for use in geometry seminars in universities and teacher-training colleges. The text can also be used as supplementary reading by high school teachers who want to extend their range of knowledge on projective transformations.
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
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Author : Michael E. Mortenson
language : en
Publisher:
Release Date : 1995
Geometric Transformations 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 1995 with Mathematics categories.
Gives the reader a full understanding of transformation theory, the role of invariants, the uses of various notation systems, and the relationships between transformations. Describes how geometric objects, or things represented as such, when subjected to mathematical operations called geometric transformations, may change position, orientation, or shape even though the properties that characterize their geometric identity and integrity remain unchanged or invariant.
Geometric Transformations
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Author : Исаак Моисеевич Яглом
language : en
Publisher: MAA Press
Release Date : 1962
Geometric Transformations written by Исаак Моисеевич Яглом and has been published by MAA Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with Mathematics categories.
Almost everyone is acquainted with plane Euclidean geometry as it is usually taught in high school. This book introduces the reader to a completely different way of looking at familiar geometrical facts. It is concerned with transformations of the plane that do not alter the shapes and sizes of geometric figures. Such transformations play a fundamental role in the group theoretic approach to geometry. The treatment is direct and simple. The reader is introduced to new ideas and then is urged to solve problems using these ideas. The problems form an essential part of this book and the solutions are given in detail in the second half of the book.
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.
Geometric Transformations
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Author : Petr Sergeevich Modenov
language : en
Publisher:
Release Date : 1961
Geometric 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 1961 with Geometry categories.
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.