TY  - BOOK
AU  - Farris,Frank A.
TI  - Creating Symmetry: The Artful Mathematics of Wallpaper Patterns 
SN  - 9780691161730
AV  - QA174.7.S96 F37 2015eb
U1  - 516/.1 23
PY  - 2015///]
CY  - Princeton, NJ : 
PB  - Princeton University Press, 
KW  - Symmetry (Art)
KW  - Symmetry (Mathematics)
KW  - ART / General
KW  - bisacsh
KW  - Abstract algebra
KW  - Addition
KW  - Algorithm
KW  - Antisymmetry
KW  - Arc length
KW  - Boundary value problem
KW  - Cartesian coordinate system
KW  - Circular motion
KW  - Circumference
KW  - Coefficient
KW  - Complex analysis
KW  - Complex multiplication
KW  - Complex number
KW  - Complex plane
KW  - Computation
KW  - Coordinate system
KW  - Coset
KW  - Cyclic group
KW  - Derivative
KW  - Diagonal
KW  - Diagram (category theory)
KW  - Dihedral group
KW  - Division by zero
KW  - Domain coloring
KW  - Dot product
KW  - Eigenfunction
KW  - Eigenvalues and eigenvectors
KW  - Eisenstein integer
KW  - Epicycloid
KW  - Equation
KW  - Euler's formula
KW  - Even and odd functions
KW  - Exponential function
KW  - Fourier series
KW  - Frieze group
KW  - Function (mathematics)
KW  - Function composition
KW  - Function space
KW  - Gaussian integer
KW  - Geometry
KW  - Glide reflection
KW  - Group (mathematics)
KW  - Group theory
KW  - Homomorphism
KW  - Horocycle
KW  - Hyperbolic geometry
KW  - Ideal point
KW  - Integer
KW  - Lattice (group)
KW  - Linear interpolation
KW  - Local symmetry
KW  - M. C. Escher
KW  - Main diagonal
KW  - Mathematical proof
KW  - Mathematical structure
KW  - Mathematics
KW  - Mirror symmetry (string theory)
KW  - Mirror symmetry
KW  - Morphing
KW  - Natural number
KW  - Normal subgroup
KW  - Notation
KW  - Ordinary differential equation
KW  - Parallelogram
KW  - Parametric equation
KW  - Parametrization
KW  - Periodic function
KW  - Plane symmetry
KW  - Plane wave
KW  - Point group
KW  - Polynomial
KW  - Power series
KW  - Projection (linear algebra)
KW  - Pythagorean triple
KW  - Quantity
KW  - Quotient group
KW  - Real number
KW  - Reciprocal lattice
KW  - Rectangle
KW  - Reflection symmetry
KW  - Right angle
KW  - Ring of integers
KW  - Rotational symmetry
KW  - Scientific notation
KW  - Special case
KW  - Square lattice
KW  - Subgroup
KW  - Summation
KW  - Symmetry group
KW  - Symmetry
KW  - Tetrahedron
KW  - Theorem
KW  - Translational symmetry
KW  - Trigonometric functions
KW  - Unique factorization domain
KW  - Unit circle
KW  - Variable (mathematics)
KW  - Vector space
KW  - Wallpaper group
KW  - Wave packet
N1  - 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; restricted access
N2  - 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
UR  - https://doi.org/10.1515/9781400865673?locatt=mode:legacy
UR  - https://www.degruyter.com/isbn/9781400865673
UR  - https://www.degruyter.com/document/cover/isbn/9781400865673/original
ER  -