Geometry and Symmetry

Front Cover
Dover Publications, 1988 - Mathematics - 288 pages

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.

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Contents

Algebraic and Combinatoric Preliminaries
1
An Introduction to Crystallography
3
Bibliography and suggestions for further reading
43
Copyright

7 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

abelian affine space affine subspace affine transformation algebraic Assume axis B₁ basis central dilatation characteristic choose collineation commutative conjugacy classes conjugate contains coordinate map coordinate system corollary correspondence crystallographic point group cube defined Definition dimension direct isometries elements equation euclidean space example exercise field F finite fixed points function ƒ and g G-orbit g₁ geometry half-turn hence homogeneous homogeneous coordinates homomorphism hyperplane implies induced inner automorphism integers intersection invariant involutions isomorphic kernel lattice group leaves left fixed lemma Let G linear transformation matrix midpoint n-dimensional nonsingular nontrivial nonzero normal subgroup P₁ permutation perpendicular perspectivity pointwise fixed polynomial problem projective plane projective space prove quadric real affine reflection rotation scalar semi-linear sending similarity space groups space over F subgroup of G subset symmetry group tion translation unique v₁ vector space vertex W₁ W₂ X₁ Y₁

Bibliographic information

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
Subjects ›  › 

Mathematics / Combinatorics
Mathematics / Geometry / General
Mathematics / Topology
Science / Physics / General
  
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