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Transformational plane geometry

Author: Ronald N Umble; Zhigang Han
Publisher: Boca Raton : CRC Press, Taylor & Francis Group, [2015]
Series: Textbooks in mathematics (Boca Raton, Fla.)
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
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Document Type: Book
All Authors / Contributors: Ronald N Umble; Zhigang Han
ISBN: 9781482234718 1482234718
OCLC Number: 883649379
Notes: "A Chapman & Hall book."
Description: xxiii, 212 pages : illustrations ; 25 cm.
Contents: Axioms of Euclidean Plane Geometry The Existence and Incidence Postulates The Distance and Ruler Postulates The Plane Separation Postulate The Protractor Postulate The Side-Angle-Side Postulate and the Euclidean Parallel Postulate Theorems of Euclidean Plane Geometry The Exterior Angle Theorem Triangle Congruence Theorems The Alternate Interior Angles Theorem and the Angle Sum Theorem Similar Triangles Introduction to Transformations, Isometries, and Similarities Transformations Isometries and Similarities Appendix: Proof of Surjectivity Translations, Rotations, and Reflections Translations Rotations Reflections Appendix: Geometer's Sketchpad Commands Required by Exploratory Activities Compositions of Translations, Rotations, and Reflections The Three Points Theorem Rotations as Compositions of Two Reflections Translations as Compositions of Two Halfturns or Two Reflections The Angle Addition Theorem Glide Reflections Classification of Isometries The Fundamental Theorem and Congruence Classification of Isometries Orientation and the Isometry Recognition Problem The Geometry of Conjugation Symmetry of Plane Figures Groups of Isometries Symmetry Type Rosettes Frieze Patterns Wallpaper Patterns Similarity Plane Similarities Classification of Dilatations Classification of Similarities and the Similarity Recognition Problem Conjugation and Similarity Symmetry Appendix: Hints and Answers to Selected Exercises Bibliography Index
Series Title: Textbooks in mathematics (Boca Raton, Fla.)
Responsibility: Ronald N. Umble, Millersville University, Millersville, PA, USA, Zhigang Han, Millersville University, Millersville, PA, USA.
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"This book is designed for a one-semester course at the junior undergraduate level and turns especially to future educators in the USA. ... The arrangement and clarity of the text meet the most Read more...

 
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