Euclidean and Transformational Geometry: A Deductive Inquiry

Author: Shlomo Libeskind

Publisher: Jones & Bartlett Publishers

ISBN: 0763762229

Category: Mathematics

Page: 371

View: 3449

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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.
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Euclidean Geometry and Transformations

Author: Clayton W. Dodge

Publisher: Courier Corporation

ISBN: 0486138429

Category: Mathematics

Page: 304

View: 8822

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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.
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Euclidean and Affine Transformations

Geometric Transformations

Author: P. S. Modenov,A. S. Parkhomenko

Publisher: Academic Press

ISBN: 1483261484

Category: Mathematics

Page: 170

View: 4160

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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.
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Advanced Euclidian Geometry

Excursions for Students and Teachers

Author: Alfred S. Posamentier

Publisher: Springer Science & Business Media

ISBN: 9781930190856

Category: Mathematics

Page: 254

View: 439

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Advanced Euclidean Geometry provides a thorough review of the essentials of high school geometry and then expands those concepts to advanced Euclidean geometry, to give teachers more confidence in guiding student explorations and questions. The text contains hundreds of illustrations created in The Geometer's Sketchpad Dynamic Geometry® software. It is packaged with a CD-ROM containing over 100 interactive sketches using SketchpadTM (assumes that the user has access to the program).
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Transformation Geometry

An Introduction to Symmetry

Author: George E. Martin

Publisher: Springer Science & Business Media

ISBN: 1461256801

Category: Mathematics

Page: 240

View: 8334

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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.
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Geometry and Its Applications

Author: Walter A. Meyer

Publisher: Elsevier

ISBN: 9780080478036

Category: Mathematics

Page: 560

View: 1473

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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
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College Geometry

A Discovery Approach

Author: David C. Kay

Publisher: Addison Wesley

ISBN: 9780321046246

Category: Mathematics

Page: 561

View: 886

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College Geometry is an approachable text, covering both Euclidean and Non-Euclidean geometry. This text is directed at the one semester course at the college level, for both pure mathematics majors and prospective teachers. A primary focus is on student participation, which is promoted in two ways: (1) Each section of the book contains one or two units, called Moments for Discovery, that use drawing, computational, or reasoning experiments to guide students to an often surprising conclusion related to section concepts; and (2) More than 650 problems were carefully designed to maintain student interest.
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Geometric Transformations IV

Circular Transformations

Author: I. M. Yaglom

Publisher: MAA

ISBN: 9780883856482

Category: Mathematics

Page: 285

View: 1452

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The familiar plane geometry of secondary school - figures composed of lines and circles - takes on a new life when viewed as the study of properties that are preserved by special groups of transformations. No longer is there a single, universal geometry: different sets of transformations of the plane correspond to intriguing, disparate geometries. This book is the concluding Part IV of Geometric Transformations, but it can be studied independently of Parts I, II, and III. The present Part IV develops the geometry of transformations of the plane that map circles to circles (conformal or anallagmatic geometry). The notion of inversion, or reflection in a circle, is the key tool employed. Applications include ruler-and-compass constructions and the Poincar model of hyperbolic geometry. The straightforward, direct presentation assumes only some background in elementary geometry and trigonometry.
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