# THEORY OF SYMMETRY

AND ORNAMENT

*Slavik Jablan*

This 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).

### CONTENTS

1. **Introduction**

2. **Theory of Isometric Symmetry Groups in ***E*^{2}
and Ornamental Art

3. **Similarity Symmetry in ***E*^{2}

4. **Conformal Symmetry in ***E*^{2}\{O}

5. **Theory of Symmetry and Ornamental Art**

*Published by
MATHEMATICAL INSTITUTE, Belgrade, 1995*

331 pages, 171 illustrations, paperbound, $30

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