Transformational Plane Geometry

Author : Ronald N. Umble,Zhigang Han
Publisher : CRC Press
Page : 235 pages
File Size : 51,9 Mb
Release : 2014-12-01
Category : Mathematics
ISBN : 9781482234725

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Transformational Plane Geometry by Ronald N. Umble,Zhigang Han Pdf

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 : Ronald N. Umble,Zhigang Han
Publisher : CRC Press
Page : 239 pages
File Size : 49,6 Mb
Release : 2014-12-01
Category : Mathematics
ISBN : 9781482234718

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Transformational Plane Geometry by Ronald N. Umble,Zhigang Han Pdf

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 : James R. King
Publisher : American Mathematical Soc.
Page : 258 pages
File Size : 44,8 Mb
Release : 2021-04-26
Category : Education
ISBN : 9781470463076

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Geometry Transformed: Euclidean Plane Geometry Based on Rigid Motions by James R. King Pdf

Many paths lead into Euclidean plane geometry. Geometry Transformed offers an expeditious yet rigorous route using axioms based on rigid motions and dilations. Since transformations are available at the outset, interesting theorems can be proved sooner; and proofs can be connected to visual and tactile intuition about symmetry and motion. The reader thus gains valuable experience thinking with transformations, a skill that may be useful in other math courses or applications. For students interested in teaching mathematics at the secondary school level, this approach is particularly useful since geometry in the Common Core State Standards is based on rigid motions. The only prerequisite for this book is a basic understanding of functions. Some previous experience with proofs may be helpful, but students can also learn about proofs by experiencing them in this book—in a context where they can draw and experiment. The eleven chapters are organized in a flexible way to suit a variety of curriculum goals. In addition to a geometrical core that includes finite symmetry groups, there are additional topics on circles and on crystallographic and frieze groups, and a final chapter on affine and Cartesian coordinates. The exercises are a mixture of routine problems, experiments, and proofs.

Author : George E. Martin
Publisher : Springer Science & Business Media
Page : 251 pages
File Size : 44,8 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 : Shlomo Libeskind
Publisher : Jones & Bartlett Publishers
Page : 381 pages
File Size : 42,9 Mb
Release : 2008-02-12
Category : Mathematics
ISBN : 9780763762223

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Euclidean and Transformational Geometry: A Deductive Inquiry by Shlomo Libeskind Pdf

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 : I. E. Leonard,J. E. Lewis,A. C. F. Liu,G. W. Tokarsky
Publisher : John Wiley & Sons
Page : 496 pages
File Size : 44,8 Mb
Release : 2014-04-30
Category : Mathematics
ISBN : 9781118679142

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Classical Geometry by I. E. Leonard,J. E. Lewis,A. C. F. Liu,G. W. Tokarsky Pdf

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 : John Charles Stone,James Franklin Millis
Publisher : Unknown
Page : 298 pages
File Size : 40,5 Mb
Release : 1916
Category : Geometry
ISBN : UOM:39015043534356

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Plane Geometry by John Charles Stone,James Franklin Millis Pdf

Author : Richard G. Brown
Publisher : Dale Seymour Publication
Page : 96 pages
File Size : 40,9 Mb
Release : 1989-01
Category : Geometry
ISBN : 0866514651

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Transformational Geometry by Richard G. Brown Pdf

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 : Vladimir V. Kisil
Publisher : World Scientific
Page : 207 pages
File Size : 40,7 Mb
Release : 2012
Category : Mathematics
ISBN : 9781848168589

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Geometry of Möbius Transformations by Vladimir V. Kisil Pdf

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.

Author : William H. Barker,Roger Howe
Publisher : American Mathematical Soc.
Page : 570 pages
File Size : 41,8 Mb
Release : 2007
Category : Geometry, Modern
ISBN : 9780821839003

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Continuous Symmetry by William H. Barker,Roger Howe Pdf

The fundamental idea of geometry is that of symmetry. With that principle as the starting point, Barker and Howe begin an insightful and rewarding study of Euclidean geometry. The primary focus of the book is on transformations of the plane. The transformational point of view provides both a path for deeper understanding of traditional synthetic geometry and tools for providing proofs that spring from a consistent point of view. As a result, proofs become more comprehensible, as techniques can be used and reused in similar settings. The approach to the material is very concrete, with complete explanations of all the important ideas, including foundational background. The discussions of the nine-point circle and wallpaper groups are particular examples of how the strength of the transformational point of view and the care of the authors' exposition combine to give a remarkable presentation of topics in geometry. This text is for a one-semester undergraduate course on geometry. It is richly illustrated and contains hundreds of exercises.

Author : Clayton W. Dodge
Publisher : Courier Corporation
Page : 306 pages
File Size : 50,5 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 : Charlotte Angas Scott
Publisher : Unknown
Page : 312 pages
File Size : 41,5 Mb
Release : 1894
Category : Geometry, Analytic
ISBN : UOM:39015064342432

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An Introductory Account of Certain Modern Ideas and Methods in Plane Analytical Geometry by Charlotte Angas Scott Pdf

Author : Edward C. Wallace,Stephen F. West
Publisher : Waveland Press
Page : 510 pages
File Size : 55,6 Mb
Release : 2015-10-23
Category : Mathematics
ISBN : 9781478632047

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Roads to Geometry by Edward C. Wallace,Stephen F. West Pdf

Now available from Waveland Press, the Third Edition of Roads to Geometry is appropriate for several kinds of students. Pre-service teachers of geometry are provided with a thorough yet accessible treatment of plane geometry in a historical context. Mathematics majors will find its axiomatic development sufficiently rigorous to provide a foundation for further study in the areas of Euclidean and non-Euclidean geometry. By using the SMSG postulate set as a basis for the development of plane geometry, the authors avoid the pitfalls of many “foundations of geometry” texts that encumber the reader with such a detailed development of preliminary results that many other substantive and elegant results are inaccessible in a one-semester course. At the end of each section is an ample collection of exercises of varying difficulty that provides problems that both extend and clarify results of that section, as well as problems that apply those results. At the end of chapters 3–7, a summary list of the new definitions and theorems of each chapter is included.

Author : Petr Sergeevich Modenov,A. S. Parkhomenko
Publisher : Unknown
Page : 156 pages
File Size : 49,5 Mb
Release : 1966
Category : Geometry, Algebraic
ISBN : UOM:39015015619219

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Geometric Transformations: Projective transformations by Petr Sergeevich Modenov,A. S. Parkhomenko Pdf

Author : Frank M. Eccles
Publisher : Unknown
Page : 177 pages
File Size : 43,8 Mb
Release : 1971
Category : Geometry, Algebraic
ISBN : 0201018519

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An Introduction to Transformational Geometry by Frank M. Eccles Pdf