Transformational Geometry PDF Download
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Author | : George E. Martin |
Publisher | : Springer Science & Business Media |
Total Pages | : 251 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461256801 |
Download Transformation Geometry Book in PDF, ePub and Kindle
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 | : Shlomo Libeskind |
Publisher | : Jones & Bartlett Publishers |
Total Pages | : 381 |
Release | : 2008-02-12 |
Genre | : Mathematics |
ISBN | : 1449650090 |
Download Euclidean and Transformational Geometry: A Deductive Inquiry Book in PDF, ePub and Kindle
Ideal for mathematics majors and prospective secondary school teachers, Euclidean and Transformational Geometry provides a complete and solid presentation of Euclidean geometry with an emphasis on solving challenging problems. The author examines various strategies and heuristics for approaching proofs and discusses the process students should follow to determine how to proceed from one step to the next through numerous problem solving techniques. A large collection of problems, varying in level of difficulty, are integrated throughout the text and suggested hints for the more challenging problems appear in the instructor's solutions manual and can be used at the instructor's discretion.
Author | : Shoshichi Kobayashi |
Publisher | : Springer Science & Business Media |
Total Pages | : 192 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642619819 |
Download Transformation Groups in Differential Geometry Book in PDF, ePub and Kindle
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 | : Ronald N. Umble |
Publisher | : CRC Press |
Total Pages | : 239 |
Release | : 2014-12-01 |
Genre | : Mathematics |
ISBN | : 1482234718 |
Download Transformational Plane Geometry Book in PDF, ePub and Kindle
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 | : Bruce Solomon |
Publisher | : CRC Press |
Total Pages | : 474 |
Release | : 2014-12-12 |
Genre | : Mathematics |
ISBN | : 1482299305 |
Download Linear Algebra, Geometry and Transformation Book in PDF, ePub and Kindle
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 | : Richard G. Brown |
Publisher | : Dale Seymour Publication |
Total Pages | : 96 |
Release | : 1989-01 |
Genre | : Geometry |
ISBN | : 9780866514651 |
Download Transformational Geometry Book in PDF, ePub and Kindle
Students explore and transform geometric shapes as they learn about maps and mappings, isometries, rotations, symmetry and groups, translations, half-turns, and transformation groups. Also useful for precalculus, short college courses, and teacher training. Exercises and answers.
Author | : Răzvan Gelca |
Publisher | : Springer Nature |
Total Pages | : 581 |
Release | : 2022-02-16 |
Genre | : Mathematics |
ISBN | : 3030891178 |
Download Geometric Transformations Book in PDF, ePub and Kindle
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 | : I. E. Leonard |
Publisher | : John Wiley & Sons |
Total Pages | : 501 |
Release | : 2014-04-30 |
Genre | : Mathematics |
ISBN | : 1118679148 |
Download Classical Geometry Book in PDF, ePub and Kindle
Features the classical themes of geometry with plentiful applications in mathematics, education, engineering, and science Accessible and reader-friendly, Classical Geometry: Euclidean, Transformational, Inversive, and Projective introduces readers to a valuable discipline that is crucial to understanding bothspatial relationships and logical reasoning. Focusing on the development of geometric intuitionwhile avoiding the axiomatic method, a problem solving approach is encouraged throughout. The book is strategically divided into three sections: Part One focuses on Euclidean geometry, which provides the foundation for the rest of the material covered throughout; Part Two discusses Euclidean transformations of the plane, as well as groups and their use in studying transformations; and Part Three covers inversive and projective geometry as natural extensions of Euclidean geometry. In addition to featuring real-world applications throughout, Classical Geometry: Euclidean, Transformational, Inversive, and Projective includes: Multiple entertaining and elegant geometry problems at the end of each section for every level of study Fully worked examples with exercises to facilitate comprehension and retention Unique topical coverage, such as the theorems of Ceva and Menalaus and their applications An approach that prepares readers for the art of logical reasoning, modeling, and proofs The book is an excellent textbook for courses in introductory geometry, elementary geometry, modern geometry, and history of mathematics at the undergraduate level for mathematics majors, as well as for engineering and secondary education majors. The book is also ideal for anyone who would like to learn the various applications of elementary geometry.
Author | : Walter A. Meyer |
Publisher | : Elsevier |
Total Pages | : 560 |
Release | : 2006-02-21 |
Genre | : Mathematics |
ISBN | : 0080478034 |
Download Geometry and Its Applications Book in PDF, ePub and Kindle
Meyer's Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry's usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers. Realistic applications integrated throughout the text, including (but not limited to): Symmetries of artistic patterns Physics Robotics Computer vision Computer graphics Stability of architectural structures Molecular biology Medicine Pattern recognition Historical notes included in many chapters
Author | : Emil Artin |
Publisher | : Courier Dover Publications |
Total Pages | : 228 |
Release | : 2016-01-20 |
Genre | : Mathematics |
ISBN | : 048680920X |
Download Geometric Algebra Book in PDF, ePub and Kindle
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.