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Symmetry: Chinese Lattice Designs The Alhambra M. C. Escher

Symmetry: Chinese Lattice Designs The Alhambra M. C. Escher. Wallpaper Designs Hungarian Needlework. also. Elliot A. Tanis Hope College.

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Symmetry: Chinese Lattice Designs The Alhambra M. C. Escher

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  1. Symmetry:Chinese Lattice DesignsThe AlhambraM. C. Escher • Wallpaper Designs • Hungarian Needlework also Elliot A. Tanis Hope College

  2. A repeating pattern or a tessellation or a tiling of the plane is a covering of the plane by one or more figures with a repeating pattern of the figures that has no gaps and no overlapping of the figures. • Equilateral triangles • Squares • Regular Hexagons Examples: Regular Polygons

  3. Some examples of periodic or repeating patterns, sometimes called “wallpaper designs,” will be shown. There are 17 “plane symmetry groups” or types of patterns.

  4. Examples of places where repeating patterns are found: • Wallpaper Designs • Chinese Lattice Designs • Hungarian Needlework • Islamic Art • The Alhambra • M. C. Escher’s Tessellations

  5. Wallpaper Designs

  6. Chinese Lattice Designs

  7. Chinese Lattice Design

  8. Chinese Garden

  9. p1 p211 p1m1 pg c1m1 p2mm p2gg p4gm p2mg p4m c2mm p4 p3 p3m1 p6 p31m p6mm

  10. p2gg p2mm p2mg p4mm p4gm p6mm p1 p4 p3m1 cm p6 p31m p2 c2mm p3 pm pg

  11. Wall Panel, Iran, 13th/14th cent(p4mm)

  12. Wall Panel, Iran, 13th/14th cent (p6mm)

  13. Design at the Alhambra

  14. Design at the Alhambra

  15. Hall of Repose - The Alhambra

  16. Hall of Repose - The Alhambra

  17. Resting Hall - The Alhambra

  18. Collage of Alhambra Tilings

  19. Church/Mosque in Cordoba

  20. Church/Mosque in Cordoba

  21. Pillars by M. C. Escher

  22. Cordoba

  23. Seville

  24. Seville

  25. M. C. Escher, 1898 - 1972

  26. Keukenhof Gardens

  27. Keukenhof Gardens

  28. Escher’s Drawings of Alhambra Repeating Patterns

  29. Escher Sketches of designs in the Alhambra and La Mezquita (Cordoba)

  30. Mathematical Reference: “The Plane Symmetry Groups: Their Recognition and Notation” by Doris Schattschneider, The Mathematical Monthly, June-July, 1978 Artistic Source: Maurits C. Escher (1898-1972) was a master at constructing tessellations

  31. Visions of Symmetry Doris Schattschneider W.H. Freeman 1990

  32. 1981, 1982, 1984, 1992

  33. A unit cell or “tile” is the smallest region in the plane having the property that the set of all of its images will fill in the plane. These images may be obtained by: • Translations • Rotations • Reflections • Glide Reflections

  34. Unit Cell -- de Porcelain Fles

  35. Translation

  36. Translation

  37. Pegasus - p1 105 D Baarn, 1959 System I

  38. Pegasus - p1

  39. Ernest R. Ranucci Joseph L. Teeters

  40. Suggestion From Ranucci and Teeters

  41. Outline Of One Pegasus

  42. Why Is Red Used?

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