Creating Symmetry : The Artful Mathematics of Wallpaper Patterns / Frank A. Farris.

Format:

Book

Author/Creator:

Farris, Frank A., author.

Language:

English

Subjects (All):

Symmetry (Mathematics).

Symmetry (Art).

Physical Description:

1 online resource (247 p.)

Edition:

Course Book

Place of Publication:

Princeton, NJ : Princeton University Press, [2015]

Language Note:

English

Summary:

This lavishly illustrated book provides a hands-on, step-by-step introduction to the intriguing mathematics of symmetry. Instead of breaking up patterns into blocks-a sort of potato-stamp method-Frank Farris offers a completely new waveform approach that enables you to create an endless variety of rosettes, friezes, and wallpaper patterns: dazzling art images where the beauty of nature meets the precision of mathematics.Featuring more than 100 stunning color illustrations and requiring only a modest background in math, Creating Symmetry begins by addressing the enigma of a simple curve, whose curious symmetry seems unexplained by its formula. Farris describes how complex numbers unlock the mystery, and how they lead to the next steps on an engaging path to constructing waveforms. He explains how to devise waveforms for each of the 17 possible wallpaper types, and then guides you through a host of other fascinating topics in symmetry, such as color-reversing patterns, three-color patterns, polyhedral symmetry, and hyperbolic symmetry. Along the way, Farris demonstrates how to marry waveforms with photographic images to construct beautiful symmetry patterns as he gradually familiarizes you with more advanced mathematics, including group theory, functional analysis, and partial differential equations. As you progress through the book, you'll learn how to create breathtaking art images of your own.Fun, accessible, and challenging, Creating Symmetry features numerous examples and exercises throughout, as well as engaging discussions of the history behind the mathematics presented in the book.

Contents:

Frontmatter

Contents

Preface

1. Going in Circles

2. Complex Numbers and Rotations

3. Symmetry of the Mystery Curve

4. Mathematical Structures and Symmetry: Groups, Vector Spaces, and More

5. Fourier Series: Superpositions of Waves

6. Beyond Curves: Plane Functions

7. Rosettes as Plane Functions

8. Frieze Functions (from Rosettes!)

9. Making Waves

10. Plane Wave Packets for 3-Fold Symmetry

11. Waves, Mirrors, and 3-Fold Symmetry

12. Wallpaper Groups and 3-Fold Symmetry

13. Forbidden Wallpaper Symmetry: 5-Fold Rotation

14. Beyond 3-Fold Symmetry: Lattices, Dual Lattices, and Waves

15. Wallpaper with a Square Lattice

16. Wallpaper with a Rhombic Lattice

17. Wallpaper with a Generic Lattice

18. Wallpaper with a Rectangular Lattice

19. Color-Reversing Wallpaper Functions

20. Color-Turning Wallpaper Functions

21. The Point Group and Counting the 17

22. Local Symmetry in Wallpaper and Rings of Integers

23. More about Friezes

24. Polyhedral Symmetry (in the Plane?)

25. Hyperbolic Wallpaper

26. Morphing Friezes and Mathematical Art

27. Epilog

A. Cell Diagrams for the 17 Wallpaper Groups

B. Recipes for Wallpaper Functions

C. The 46 Color-Reversing Wallpaper Types

Bibliography

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 23. Mai 2019)

OCLC:

906026369