Farris, Frank A.,
Creating symmetry : the artful mathematics of wallpaper patterns / Frank A. Farris. - 1 online resource (xiii, 230 pages) : illustrations (chiefly color)
Includes bibliographical references and index.
Cover ; Title ; Copyright; 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 Waves15 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 FunctionsC The 46 Color-ReversingWallpaper Types; Bibliography; Index.
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 cur.
9781400865673 1400865670
22573/ctv7grtzb JSTOR 9453365 IEEE
2014040468
Symmetry (Mathematics)
Symmetry (Art)
Sym�etrie (Math�ematiques)
Sym�etrie (Art)
MATHEMATICS--Geometry--General.
ART--General.
Symmetry (Art)
Symmetry (Mathematics)
Electronic books.
QA174.7.S96 / F37 2015eb
516/.1
Creating symmetry : the artful mathematics of wallpaper patterns / Frank A. Farris. - 1 online resource (xiii, 230 pages) : illustrations (chiefly color)
Includes bibliographical references and index.
Cover ; Title ; Copyright; 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 Waves15 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 FunctionsC The 46 Color-ReversingWallpaper Types; Bibliography; Index.
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 cur.
9781400865673 1400865670
22573/ctv7grtzb JSTOR 9453365 IEEE
2014040468
Symmetry (Mathematics)
Symmetry (Art)
Sym�etrie (Math�ematiques)
Sym�etrie (Art)
MATHEMATICS--Geometry--General.
ART--General.
Symmetry (Art)
Symmetry (Mathematics)
Electronic books.
QA174.7.S96 / F37 2015eb
516/.1