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Undergraduate Texts in Mathematics Ser.: Transformation Geometry : An Introduction to Symmetry by George E. Martin (1996, Hardcover)

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This textbook, titled "Transformation Geometry: An Introduction to Symmetry," is a valuable resource for students studying geometry. Written by George E. Martin and published by Springer New York in 1996, this book is a hardcover with a length of 9.2 inches and a width of 6.1 inches. The book is part of the Undergraduate Texts in Mathematics Ser. and contains XII, 240 pages. The focus of this book is on transformation geometry and symmetry, making it an ideal textbook for students studying geometry. It is available in English and is categorized under Books & Magazines, Textbooks, Education & Reference, and Textbooks.

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Product Information

Transformation geometry is a relatively recent expression of the successful venture of bringing together geometry and algebra. The name describes an approach as much as the content. Our subject is Euclidean geometry. Essential to the study of the plane or any mathematical system is an under- standing of the transformations on that system that preserve designated features of the system. Our study of the automorphisms of the plane and of space is based on only the most elementary high-school geometry. In particular, group theory is not a prerequisite here. On the contrary, this modern approach to Euclidean geometry gives the concrete examples that are necessary to appreciate an introduction to group theory. Therefore, a course based on this text is an excellent prerequisite to the standard course in abstract algebra taken by every undergraduate mathematics major. An advantage of having nb college mathematics prerequisite to our study is that the text is then useful for graduate mathematics courses designed for secondary teachers. Many of the students in these classes either have never taken linear algebra or else have taken it too long ago to recall even the basic ideas. It turns out that very little is lost here by not assuming linear algebra. A preliminary version of the text was written for and used in two courses-one was a graduate course for teachers and the other a sophomore course designed for the prospective teacher and the general mathematics major taking one course in geometry.

Product Identifiers

Publisher
Springer New York
ISBN-10
0387906363
ISBN-13
9780387906362
eBay Product ID (ePID)
145574

Product Key Features

Author
George E. Martin
Publication Name
Transformation Geometry : an Introduction to Symmetry
Format
Hardcover
Language
English
Publication Year
1996
Series
Undergraduate Texts in Mathematics Ser.
Type
Textbook
Number of Pages
Xii, 240 Pages

Dimensions

Item Length
9.2in
Item Width
6.1in
Item Weight
42 Oz

Additional Product Features

Number of Volumes
1 Vol.
Lc Classification Number
Qa440-699
Table of Content
1 Introduction.- 1.1 Transformations and Collineations.- 1.2 Geometric Notation.- 1.3 Exercises.- 2 Properties of Transformations.- 2.1 Groups of Transformations.- 2.2 Involutions.- 2.3 Exercises.- 3 Translations and Halfturns.- 3.1 Translations.- 3.2 Halfturns.- 3.3 Exercises.- 4 Reflections.- 4.1 Equations for a Reflection.- 4.2 Properties of a Reflection.- 4.3 Exercises.- 5 Congruence.- 5.1 Isometries as Products of Reflections.- 5.2 Paper Folding Experiments and Rotations.- 5.3 Exercises.- 6 The Product of Two Reflections.- 6.1 Translations and Rotations.- 6.2 Fixed Points and Involutions.- 6.3 Exercises.- 7 Even Isometries.- 7.1 Parity.- 7.2 The Dihedral Groups.- 7.3 Exercises.- 8 Classification of Plane Isometries.- 8.1 Glide Reflections.- 8.2 Leonardo's Theorem.- 8.3 Exercises.- 9 Equations for Isometries.- 9.1 Equations.- 9.2 Supplementary Exercises (Chapter 1-8).- 9.3 Exercises.- 10 The Seven Frieze Groups.- 10.1 Frieze Groups.- 10.2 Frieze Patterns.- 10.3 Exercises.- 11 The Seventeen Wallpaper Groups.- 11.1 The Crystallographic Restriction.- 11.2 Wallpaper Groups and Patterns.- 11.3 Exercises.- 12 Tessellations.- 12.1 Tiles.- 12.2 Reptiles.- 12.3 Exercises.- 13 Similarities on the Plane.- 13.1 Classification of Similarities.- 13.2 Equations for Similarities.- 13.3 Exercises.- 14 Classical Theorems.- 14.1 Menelaus, Ceva, Desargues, Pappus, Pascal.- 14.2 Euler, Brianchon, Poncelet, Feuerbach.- 14.3 Exercises.- 15 Affine Transformations.- 15.1 Collineations.- 15.2 Linear Transformations.- 15.3 Exercises.- 16 Transformations on Three-space.- 16.1 Isometries on Space.- 16.2 Similarities on Space.- 16.3 Exercises.- 17 Space and Symmetry.- 17.1 The Platonic Solids.- 17.2 Finite Symmetry Groups on Space.- 17.3 Exercises.- Hints and Answers.- Notation Index.
Copyright Date
1982
Topic
Geometry / General, Transformations, Physics / General
Intended Audience
Scholarly & Professional
Illustrated
Yes
Genre
Science, Mathematics

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Undergraduate Texts in Mathematics Ser.: Transformation Geometry : An Introduction to Symmetry by George E. Martin (1996, Hardcover)

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