Geometry and Symmetry

Front Cover
Dover Publications, 1988 - Geometry, Affine - 288 pages
0 Reviews
Reviews aren't verified, but Google checks for and removes fake content when it's identified

This book is an introduction to the geometry of Euclidean, affine, and projective spaces with special emphasis on the important groups of symmetries of these spaces. The two major objectives of the text are to introduce the main ideas of affine and projective spaces and to develop facility in handling transformations and groups of transformations. Since there are many good texts on affine and projective planes, the author has concentrated on the "n"-dimensional cases.
Designed to be used in advanced undergraduate mathematics or physics courses, the book focuses on "practical geometry," emphasizing topics and techniques of maximal use in all areas of mathematics. These topics include:
Algebraic and Combinatoric Preliminaries
Isometries and Similarities
An Introduction to Crystallography
Fields and Vector Spaces
Affine Spaces
Projective Spaces
Special features include a spiral approach to symmetry; a review of the algebraic prerequisites; proofs which do not appear in other texts, such as the Polya-Burnside theorem; an extensive bibliography; and a large collection of exercises together with suggestions for term-paper topics. In addition, special emphasis is placed on the geometric significance of cosets and conjugates in a group.

From inside the book

 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Algebraic and Combinatoric Preliminaries
1
Bibliography and suggestions for further reading
83
An Introduction to Crystallography
86
Copyright

8 other sections not shown

Other editions - View all

Geometry and Symmetry
Paul B. Yale
Limited preview - 2014
Geometry and Symmetry
Paul B. Yale
Snippet view - 1968
Geometry and Symmetry
Paul B. Yale
No preview available - 2004

Common terms and phrases

addition affine space affine subspace affine transformation algebraic Assume automorphism axis basis called Chapter characteristic choose classes Clearly collineation commutative complete conjugate consider contains coordinate map corollary correspondence defined Definition determined dilatation dimension direct discrete distinct elements equation euclidean exactly example exercise fact field Figure finite fixed points function G-orbit geometry given hence homogeneous homomorphism hyperplane illustrations implies independent induced integers intersection invariant inversion involution isometries isomorphic lattice group least leaves linear transformation matrix multiplication n-dimensional natural nonzero Note origin p-matrix parallel permutation perspectivity point group polynomial possible preserves problem projective plane projective space Proof prove reflection represented respectively result rotation scalar sending Show similarity space groups subgroup symmetries Table theorem tion translation unique unit vector space W₁ W₂

Bibliographic information

QR code for Geometry and Symmetry
TitleGeometry and Symmetry
Dover Books on Mathematics Series
Dover books on advanced mathematics
Holden-Day series in mathematics
AuthorPaul B. Yale
Edition2, illustrated, unabridged, reprint
PublisherDover Publications, 1988
Original fromthe University of Michigan
DigitizedFeb 5, 2010
ISBN0486657795, 9780486657790
Length288 pages
  
Export CitationBiBTeX EndNote RefMan