Euclidean Geometry and Transformations

ISBN-10: 0486434761

ISBN-13: 9780486434766

Edition: 2004

Authors: Clayton W. Dodge
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Description: "A good textbook."--Mathematical Gazette This introduction to Euclidean geometry emphasizes both the theory and the practical application of isometries and similarities to geometric transformations. Each chapter begins with an optional commentary on the history of geometry. Contents include modern elementary geometry, isometries and similarities in the plane, vectors and complex numbers in geometry, inversion, and isometries in space. Numerous exercises appear throughout the text, many of which have corresponding answers and hints at the back of the book. Prerequisites for this text, which is suitable for undergraduate courses, include high school algebra, geometry, and elementary trigonometry. 1972 ed.

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Book details

List price: $22.95
Copyright year: 2004
Publisher: Dover Publications, Incorporated
Publication date: 5/18/2004
Binding: Paperback
Pages: 304
Size: 6.00" wide x 9.00" long x 0.75" tall
Weight: 0.836
Language: English

Modern Elementary Geometry
The Beginnings of Geometry
Directed segments and angles
Ideal points and ratios
The theorem of Menelaus
Ceva's theorem
Some geometry of the triangle
More geometry of the triangle
Geometric constructions
Isometries in the Plane
The Amazing Greeks
Introduction to translations, rotations, and reflections
Introduction to isometries
Transformation theory
Isometries as products of reflections
Translations and rotations
Halfturns
Products of reflections
Properties of isometries; a summary
Applications of isometries to elementary geometry
Further elementary applications
Advanced applications
Analytic representations of direct isometries
Analytic representations of opposite isometries
Similarities in the Plane
The rebirth of mathematical thinking
Introduction to similarities
Homothety
Similarity
Applications of similarities to elementary geometry
Further elementary applications
Advanced applications
Analytic representations of similarities
Vectors and Complex Numbers in Geometry
The search for the meaning of complex numbers
Introduction to complex numbers
Vectors
Vector multiplication
Vectors and complex numbers
Triangles in the Gauss plane
Lines in the Gauss plane
The circle
Isometries and similarities in the Gauss plane
Inversion
Matchless modern mathematics
Inversion
Progressions, ratios, and Peaucellier's cell
Inversion and complex geometry
Applications of inversion
Isometries in Space
What next?
Introduction to three dimensions
Reflection in a plane
Basic space isometries
More space isometries
Some applications
Analytic representations
Appendixes
A Summary of Book I of Euclid's Elements
Basic Ruler and Compass Constructions
Bibliography
Hints for Selected Exercises
Answers
Index
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