SYMMETRY
AND ORNAMENT Electronic reprint, copyright 1995, Slavik V. Jablan Book "Theory of Symmetry and Ornament", 331 pages, originally published on paper by the Mathematical Institute, Belgrade, Yugoslavia, 1995 Library of Congress Catalog Card Number 96-217270 ISBN 86-80593-17-6 DESCRIPTION: The book represents a comparative analysis of the theory of discrete and visually presentable continuous symmetry groups in Euclidean plane E^{2} or in E^{2}\{O}: Symmetry Groups of Rosettes, Friezes, and Ornaments (Chapter 2), Similarity Symmetry Groups in E^{2} (Chapter 3), Conformal Symmetry Groups in E^{2}\{O} (Chapter 4) and ornamental motifs found in ornamental art that satisfy the mentioned forms of symmetry. In each chapter symmetric forms are treated from the theory of groups point of view: generators, abstract definitions, structures, Cayley diagrams, data on enantiomorphism, form of the fundamental region... The analysis of the origin of corresponding symmetry structures in ornamental art: chronology of ornaments, construction problems, visual characteristics, and their relation to geometric-algebraic properties of the considered symmetry is given. The discussion is followed by illustrations, such as Cayley diagrams and ornaments.
The most of ornamental examples in the book date from prehistoric
or ancient cultures. By iterpreting the ornamental art "as the
oldest aspect of higher mathematics given implicitly", the
emphasis is on the path leading from the theory of symmetry
(i.e., the derivation, classification and analysis of symmetry
groups) toward ornaments understood as the visual
interpretations of abstract geometric-algebraic structures and
vice versa. Such an approach is becoming increasingly more
important, since it makes possible the use of visually presented
symmetry groups in all fields of science and art where there is a
need for the visual representation and analysis of symmetry
structures (Mathematics, Crystallography, Physics, Chemistry,
Biology, Applied Arts, Archaeology, Design, Architecture, Visual
Arts).
WHERE TO ORDER:
Mathematical Institute
CONTENTS:
Preface
Chapter 1: Introduction
§ 1.1. Geometry and Its Basic Terms
Chapter 2 : Theory of Isometric Symmetry Groups in E^{2} and Ornamental Art
§ 2.1. Symmetry Groups of Rosettes G_{20}
Chapter 3 : Similarity Symmetry in E^{2}
§ 3.1. Similarity Symmetry Groups of Rosettes S_{20}
Chapter 4 : Conformal Symmetry in E^{2}\{O}
§ 4.1. Conformal Symmetry Groups in E^{2}\{O}
Chapter 5 : The Theory of Symmetry and Ornamental Art
References
Notation Index
Index |