Creating Symmetry : : The Artful Mathematics of Wallpaper Patterns / / Frank A. Farris.
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 r...
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Farris, Frank A., author. aut http://id.loc.gov/vocabulary/relators/aut Creating Symmetry : The Artful Mathematics of Wallpaper Patterns / Frank A. Farris. Course Book Princeton, NJ : Princeton University Press, [2015] ©2015 1 online resource (248 p.) : 103 color illus. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda 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 http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 27. Jan 2023) Symmetry (Art). Symmetry (Mathematics). ART / General. bisacsh Abstract algebra. Addition. Algorithm. Antisymmetry. Arc length. Boundary value problem. Cartesian coordinate system. Circular motion. Circumference. Coefficient. Complex analysis. Complex multiplication. Complex number. Complex plane. Computation. Coordinate system. Coset. Cyclic group. Derivative. Diagonal. Diagram (category theory). Dihedral group. Division by zero. Domain coloring. Dot product. Eigenfunction. Eigenvalues and eigenvectors. Eisenstein integer. Epicycloid. Equation. Euler's formula. Even and odd functions. Exponential function. Fourier series. Frieze group. Function (mathematics). Function composition. Function space. Gaussian integer. Geometry. Glide reflection. Group (mathematics). Group theory. Homomorphism. Horocycle. Hyperbolic geometry. Ideal point. Integer. Lattice (group). Linear interpolation. Local symmetry. M. C. Escher. Main diagonal. Mathematical proof. Mathematical structure. Mathematics. Mirror symmetry (string theory). Mirror symmetry. Morphing. Natural number. Normal subgroup. Notation. Ordinary differential equation. Parallelogram. Parametric equation. Parametrization. Periodic function. Plane symmetry. Plane wave. Point group. Polynomial. Power series. Projection (linear algebra). Pythagorean triple. Quantity. Quotient group. Real number. Reciprocal lattice. Rectangle. Reflection symmetry. Right angle. Ring of integers. Rotational symmetry. Scientific notation. Special case. Square lattice. Subgroup. Summation. Symmetry group. Symmetry. Tetrahedron. Theorem. Translational symmetry. Trigonometric functions. Unique factorization domain. Unit circle. Variable (mathematics). Vector space. Wallpaper group. Wave packet. Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2014-2015 9783110665925 print 9780691161730 https://doi.org/10.1515/9781400865673?locatt=mode:legacy https://www.degruyter.com/isbn/9781400865673 Cover https://www.degruyter.com/document/cover/isbn/9781400865673/original |
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English |
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eBook |
author |
Farris, Frank A., Farris, Frank A., |
spellingShingle |
Farris, Frank A., Farris, Frank A., Creating Symmetry : The Artful Mathematics of Wallpaper Patterns / 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 |
author_facet |
Farris, Frank A., Farris, Frank A., |
author_variant |
f a f fa faf f a f fa faf |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Farris, Frank A., |
title |
Creating Symmetry : The Artful Mathematics of Wallpaper Patterns / |
title_sub |
The Artful Mathematics of Wallpaper Patterns / |
title_full |
Creating Symmetry : The Artful Mathematics of Wallpaper Patterns / Frank A. Farris. |
title_fullStr |
Creating Symmetry : The Artful Mathematics of Wallpaper Patterns / Frank A. Farris. |
title_full_unstemmed |
Creating Symmetry : The Artful Mathematics of Wallpaper Patterns / Frank A. Farris. |
title_auth |
Creating Symmetry : The Artful Mathematics of Wallpaper Patterns / |
title_alt |
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 |
title_new |
Creating Symmetry : |
title_sort |
creating symmetry : the artful mathematics of wallpaper patterns / |
publisher |
Princeton University Press, |
publishDate |
2015 |
physical |
1 online resource (248 p.) : 103 color illus. |
edition |
Course 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 |
isbn |
9781400865673 9783110665925 9780691161730 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA174 |
callnumber-sort |
QA 3174.7 S96 F37 42015EB |
url |
https://doi.org/10.1515/9781400865673?locatt=mode:legacy https://www.degruyter.com/isbn/9781400865673 https://www.degruyter.com/document/cover/isbn/9781400865673/original |
illustrated |
Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
516 - Geometry |
dewey-full |
516/.1 |
dewey-sort |
3516 11 |
dewey-raw |
516/.1 |
dewey-search |
516/.1 |
doi_str_mv |
10.1515/9781400865673?locatt=mode:legacy |
oclc_num |
984643798 |
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Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2014-2015 |
is_hierarchy_title |
Creating Symmetry : The Artful Mathematics of Wallpaper Patterns / |
container_title |
Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2014-2015 |
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Cell Diagrams for the 17 Wallpaper Groups -- </subfield><subfield code="t">B. Recipes for Wallpaper Functions -- </subfield><subfield code="t">C. The 46 Color-Reversing Wallpaper Types -- </subfield><subfield code="t">Bibliography -- </subfield><subfield code="t">Index</subfield></datafield><datafield tag="506" ind1="0" ind2=" "><subfield code="a">restricted access</subfield><subfield code="u">http://purl.org/coar/access_right/c_16ec</subfield><subfield code="f">online access with authorization</subfield><subfield code="2">star</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This lavishly illustrated book provides a hands-on, step-by-step introduction to the intriguing mathematics of symmetry. 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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.</subfield></datafield><datafield tag="538" ind1=" " ind2=" "><subfield code="a">Mode of access: Internet via World Wide Web.</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">In English.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Description based on online resource; title from PDF title page (publisher's Web site, viewed 27. 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C. Escher.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Main diagonal.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Mathematical proof.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Mathematical structure.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Mathematics.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Mirror symmetry (string theory).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Mirror symmetry.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Morphing.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Natural number.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Normal subgroup.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Notation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Ordinary differential equation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Parallelogram.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Parametric equation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Parametrization.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Periodic function.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Plane symmetry.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Plane wave.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Point group.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Polynomial.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Power series.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Projection (linear algebra).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Pythagorean triple.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Quantity.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Quotient group.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Real number.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Reciprocal lattice.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Rectangle.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Reflection symmetry.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Right angle.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Ring of integers.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Rotational symmetry.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Scientific notation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Special case.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Square lattice.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Subgroup.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Summation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Symmetry group.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Symmetry.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Tetrahedron.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Theorem.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Translational symmetry.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Trigonometric functions.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Unique factorization domain.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Unit circle.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Variable (mathematics).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Vector space.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Wallpaper group.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Wave packet.</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">Princeton University Press Complete eBook-Package 2014-2015</subfield><subfield code="z">9783110665925</subfield></datafield><datafield tag="776" ind1="0" ind2=" "><subfield code="c">print</subfield><subfield code="z">9780691161730</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/9781400865673?locatt=mode:legacy</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://www.degruyter.com/isbn/9781400865673</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="3">Cover</subfield><subfield code="u">https://www.degruyter.com/document/cover/isbn/9781400865673/original</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">978-3-11-066592-5 Princeton University Press Complete eBook-Package 2014-2015</subfield><subfield code="c">2014</subfield><subfield code="d">2015</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_BACKALL</subfield></datafield><datafield tag="912" ind1=" " 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