Geometric Transformations

Author : Răzvan Gelca,Ionuţ Onişor,Carlos Yuzo Shine
Publisher : Springer Nature
Page : 581 pages
File Size : 52,9 Mb
Release : 2022-02-16
Category : Mathematics
ISBN : 9783030891176

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Geometric Transformations by Răzvan Gelca,Ionuţ Onişor,Carlos Yuzo Shine Pdf

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.

Author : Isaak Moiseevich I︠A︡glom
Publisher : Unknown
Page : 152 pages
File Size : 50,6 Mb
Release : 1962
Category : Transformations (Mathematics)
ISBN : UOM:39015049377784

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Geometric Transformations by Isaak Moiseevich I︠A︡glom Pdf

Author : Michael E. Mortenson
Publisher : Unknown
Page : 376 pages
File Size : 48,9 Mb
Release : 2007
Category : Computers
ISBN : UOM:39015070694479

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Geometric Transformations for 3D Modeling by Michael E. Mortenson Pdf

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.

Author : I. M. Yaglom
Publisher : MAA
Page : 302 pages
File Size : 43,6 Mb
Release : 2009-10-15
Category : Mathematics
ISBN : 0883856484

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Geometric Transformations IV by I. M. Yaglom Pdf

A comprehensive treatment of the geometry of circular transformations.

Author : Emil Artin
Publisher : Courier Dover Publications
Page : 228 pages
File Size : 44,5 Mb
Release : 2016-01-20
Category : Mathematics
ISBN : 9780486809205

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Geometric Algebra by Emil Artin Pdf

This concise classic presents advanced undergraduates and graduate students in mathematics with an overview of geometric algebra. The text originated with lecture notes from a New York University course taught by Emil Artin, one of the preeminent mathematicians of the twentieth century. The Bulletin of the American Mathematical Society praised Geometric Algebra upon its initial publication, noting that "mathematicians will find on many pages ample evidence of the author's ability to penetrate a subject and to present material in a particularly elegant manner." Chapter 1 serves as reference, consisting of the proofs of certain isolated algebraic theorems. Subsequent chapters explore affine and projective geometry, symplectic and orthogonal geometry, the general linear group, and the structure of symplectic and orthogonal groups. The author offers suggestions for the use of this book, which concludes with a bibliography and index.

Author : Clayton W. Dodge
Publisher : Courier Corporation
Page : 306 pages
File Size : 40,5 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486138428

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Euclidean Geometry and Transformations by Clayton W. Dodge Pdf

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.

Author : Bruce Solomon
Publisher : CRC Press
Page : 474 pages
File Size : 44,8 Mb
Release : 2014-12-12
Category : Mathematics
ISBN : 9781482299304

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Linear Algebra, Geometry and Transformation by Bruce Solomon Pdf

The Essentials of a First Linear Algebra Course and MoreLinear Algebra, Geometry and Transformation provides students with a solid geometric grasp of linear transformations. It stresses the linear case of the inverse function and rank theorems and gives a careful geometric treatment of the spectral theorem.An Engaging Treatment of the Interplay amo

Author : Frederickson Greg N
Publisher : World Scientific
Page : 432 pages
File Size : 41,8 Mb
Release : 2017-11-24
Category : Mathematics
ISBN : 9789813220492

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Ernest Irving Freese's "Geometric Transformations": The Man, The Manuscript, The Magnificent Dissections! by Frederickson Greg N Pdf

A geometric dissection is a cutting of a geometric figure (such as a regular polygon, or a star, or a cross) into pieces that we can rearrange to form another geometric figure. The best dissections are beautiful and possess economy (few pieces), symmetry, or hingeability. They are often challenging to discover. Ernest Irving Freese was an architect who lived and worked in Los Angeles until his death in 1957. Shortly before he passed away, he completed a 200-page manuscript on geometric dissection, the first book-length treatment on that subject. Freese included elegant drawings of dissections that were both original and clever. After his death the manuscript lay forgotten in his former house until Greg Frederickson set in motion its recovery in 2003. What a treat that it was rescued! Frederickson's book sketches a history of geometric dissections and a biography of Freese, followed by a refurbished copy of Freese's manuscript interleaved with a commentary that highlights Freese's major contributions as well as singular improvements made by Frederickson and others after Freese. This book introduces Freese and his creations to math puzzle enthusiasts, by way of his engaging manuscript, his wild adventures, and his lovely dissections. Frederickson also includes remarkable designs that improve on Freese's work, and packs this book with nifty illustrations and tidbits that may well leave you speechless! Contents: The Rich History of Geometric DissectionsThe "Wild Adventures" of Ernest FreeseTechniques, Special Properties, HardnessFreese's Title Page and IndexIsosceles TrianglesEquilateral TrianglesSquares, Crosses, RectanglesPentagons and PentagramsHexagons and HexagramsOctagons and OctagramsEnneagons (Nonagons)Decagons and DecagramsDodecagons, DodecagramsMany-sided PolygonsMiscellaneous FiguresMore CrossesMore Miscellaneous FiguresMixed Polygons to OneSpecial Triangles Readership: General public and math puzzle enthusiasts. Keywords: Geometric Dissections;Hinged Dissections;Ernest Irving Freese;Henry E Dudeney;Mathematical Recreations;Polygons;Stars;Tessellations;Rhombuses;SymmetryReview: Key Features: The book is a feast for the eyes: Freese's manuscript displays exquisite drawings in an architect's style, while the commentary presents outstandinging dissections that illustrate a brilliant visual one-ups-man-shipThe book stretches the boundaries of dissection: Freese's manuscript explores a remarkable variety of here-to-fore unseen geometric dissections, including those that demonstrate nontrivial numerical identities. The commentary pushes his exploratory use of hinges in extraordinary ways, and drastically improves on his pioneering dissections of many-sided polygons to squaresThe book provides not only historical perspectives on geometric dissection, but also summarizes current mathematical characterizations of the hardness of minimizing the number of pieces in a dissection and of verifying motion planning of hinged dissections

Author : Feyzi Başar,Hemen Dutta
Publisher : CRC Press
Page : 173 pages
File Size : 48,5 Mb
Release : 2020-02-04
Category : Mathematics
ISBN : 9781351166911

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Summable Spaces and Their Duals, Matrix Transformations and Geometric Properties by Feyzi Başar,Hemen Dutta Pdf

The aim of Summable Spaces and Their Duals, Matrix Transformations and Geometric Properties is to discuss primarily about different kinds of summable spaces, compute their duals and then characterize several matrix classes transforming one summable space into other. The book also discusses several geometric properties of summable spaces, as well as dealing with the construction of summable spaces using Orlicz functions, and explores several structural properties of such spaces. Each chapter contains a conclusion section highlighting the importance of results, and points the reader in the direction of possible new ideas for further study. Features Suitable for graduate schools, graduate students, researchers and faculty, and could be used as a key text for special Analysis seminars Investigates different types of summable spaces and computes their duals Characterizes several matrix classes transforming one summable space into other Discusses several geometric properties of summable spaces Examines several possible generalizations of Orlicz sequence spaces

Author : David Salomon
Publisher : Springer Science & Business Media
Page : 882 pages
File Size : 54,8 Mb
Release : 1999
Category : Computers
ISBN : 0387986820

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Computer Graphics and Geometric Modeling by David Salomon Pdf

This comprehensive reference for professionals and students in the computer graphics field clearly explains how graphics programs work and how they generate realistic objects and animations. Topics include scan conversion methods, translations, rotations, moving in 3D, and perspective projections. The mathematics and geometry behind the computer graphics are also presented.

Author : George E. Martin
Publisher : Springer Science & Business Media
Page : 251 pages
File Size : 43,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461256809

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Transformation Geometry by George E. Martin Pdf

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.

Author : Shoshichi Kobayashi
Publisher : Springer Science & Business Media
Page : 192 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642619816

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Transformation Groups in Differential Geometry by Shoshichi Kobayashi Pdf

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 : Anthony J. Pettofrezzo
Publisher : Courier Corporation
Page : 225 pages
File Size : 47,9 Mb
Release : 2012-05-04
Category : Mathematics
ISBN : 9780486151809

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Matrices and Transformations by Anthony J. Pettofrezzo Pdf

This book presents an elementary and concrete approach to linear algebra that is both useful and essential for the beginning student and teacher of mathematics. Here are the fundamental concepts of matrix algebra, first in an intuitive framework and then in a more formal manner. A Variety of interpretations and applications of the elements and operations considered are included. In particular, the use of matrices in the study of transformations of the plane is stressed. The purpose of this book is to familiarize the reader with the role of matrices in abstract algebraic systems, and to illustrate its effective use as a mathematical tool in geometry. The first two chapters cover the basic concepts of matrix algebra that are important in the study of physics, statistics, economics, engineering, and mathematics. Matrices are considered as elements of an algebra. The concept of a linear transformation of the plane and the use of matrices in discussing such transformations are illustrated in Chapter #. Some aspects of the algebra of transformations and its relation to the algebra of matrices are included here. The last chapter on eigenvalues and eigenvectors contains material usually not found in an introductory treatment of matrix algebra, including an application of the properties of eigenvalues and eigenvectors to the study of the conics. Considerable attention has been paid throughout to the formulation of precise definitions and statements of theorems. The proofs of most of the theorems are included in detail in this book. Matrices and Transformations assumes only that the reader has some understanding of the basic fundamentals of vector algebra. Pettofrezzo gives numerous illustrative examples, practical applications, and intuitive analogies. There are many instructive exercises with answers to the odd-numbered questions at the back. The exercises range from routine computations to proofs of theorems that extend the theory of the subject. Originally written for a series concerned with the mathematical training of teachers, and tested with hundreds of college students, this book can be used as a class or supplementary text for enrichments programs at the high school level, a one-semester college course, individual study, or for in-service programs.

Author : Michael E. Mortenson
Publisher : Unknown
Page : 392 pages
File Size : 41,7 Mb
Release : 1995
Category : Mathematics
ISBN : UOM:39015034871593

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Geometric Transformations by Michael E. Mortenson Pdf

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.

Author : Исаак Моисеевич Яглом
Publisher : Unknown
Page : 252 pages
File Size : 55,7 Mb
Release : 1973
Category : Transformations (Mathematics)
ISBN : STANFORD:36105002018849

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Geometric Transformations by Исаак Моисеевич Яглом Pdf