PAGE 2008 - Bonner

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PAGE 2008 - Bonner

  1. 1. The Polygonal Technique The traditional use of polygonal matrices in the design of Islamic geometric patterns. Jay Bonner Design Consultant Santa Fe, New Mexico USA Email: [email_address] Web Site: www.bonner-design.com
  2. 2. Pattern Derivation – Compass-Work: Great Mosque of Damascus (715 C.E.), Pierced Stone Screen
  3. 3. Pattern Derivation – Compass-Work: Patterns are created by placing the compass at key points upon a tessellating polygonal grid
  4. 4. Pattern Derivation – Compass-Work: Quran of Ibn al-Bawwab (1000-1001 C.E.)
  5. 5. Pattern Derivation – Graph Paper Technique:
  6. 6. Pattern Derivation - Parallel Radii Technique
  7. 7. Pattern Derivation - Parallel Radii Technique
  8. 8. Pattern Derivation – Parallel Radii Technique: Sultan Han, Aksaray, Turkey (1229 C.E.)
  9. 9. Pattern Derivation – Additive Technique
  10. 10. Pattern Derivation – Point Joining
  11. 11. Pattern Derivation – Point Joining
  12. 12. Pattern Derivation – Comparative Methods
  13. 13. Pattern Derivation – Polygonal Technique The Four Pattern Families
  14. 14. The Polygonal Technique: Historical Evidence Mamluk stone work: Sultan Hassan Madrasa, Cairo (1363 C.E.)
  15. 15. The Polygonal Technique: Historical Evidence Mamluk historical example with scribed “dead-lines” under the painting.
  16. 16. The Polygonal Technique: Historical Evidence 15 th Century Mughal Jali Screen, Probably Fatipur Sikri, Agra, India
  17. 17. The Polygonal Technique: Historical Evidence One of 24 examples of the Polygonal Technique from the Topkapi Scroll. Fifteenth or sixteenth century: Western Persia.
  18. 18. Polygonal Technique The Classic 5-Fold Acute Pattern
  19. 19. Polygonal Technique The Classic 5-Fold Middle Pattern
  20. 20. Polygonal Technique The Classic 5-Fold Obtuse Pattern
  21. 21. Polygonal Technique The Classic 5-Fold 2-Point Pattern
  22. 22. 5-Fold System – the Classic Acute Pattern: Qala-i Bust, Bust, Iran (c. 1000 C.E.)
  23. 23. 5-Fold System – the Classic 2-Point Pattern: Inlay Work, Egypt, 16 th Century C.E.
  24. 24. The Polygonal Technique A Single Pattern Can Sometimes Be Produced From More Than A One Sub-Grid. The Ring of Pentagons allows for tremendous design versatility.
  25. 25. The Polygonal Technique Variations to the Pattern Lines within the Ring of Pentagons
  26. 26. 3-Fold Sub-Grid 12 Non-Regular Pentagons around a Regular Dodecagon
  27. 27. 3-Fold Pattern with 12-Pointed Stars Pattern Derivation
  28. 28. 3-Fold Pattern: 12-Pointed Stars Sub-Grid Construction Note: Three Pentagons Together are Common in 3-Fold Sub-Grids
  29. 29. Compound Pattern – 10s and 12s:
  30. 30. Compound Pattern – 10s and 12s: Topkapi Scroll with Variation at the Three Touching Pentagons
  31. 31. Compound Pattern – 10s and 12s: Sub-Grid Note: the Proportion of the Rectangular Repeat Unit is a Direct Result of the Compounded 10-Fold and 12-Fold Symmetry
  32. 32. Compound Pattern – 10s and 12s: Pattern Derivation
  33. 33. Sub-Grid Construction: 10s and 12s: Note: The Problem of the Non-Aligning Edges is Overcome by the Ring-of-Pentagons
  34. 34. Compound Pattern – 11s and 13s: A particularly complex and beautiful compound pattern is found at the Tomb of Mu’minah Khatun, Nakhichevan, Azerbaijan.
  35. 35. Compound Pattern – 11s and 13s: Detail from the Tomb of Mu’minah Khatujn, Nakhichevan, Azerbaijan. This compound Islamic geometric pattern exemplifies the highest expression of this art form.
  36. 36. Compound Pattern – 11s and 13s: Once Again, Two Different Elongated Hexagons as the Repeat Unit Having Equally 11-Fold and 13-Fold Symmetry!
  37. 37. Compound Pattern – 11s and 13s: Pattern Derivation
  38. 38. Sub-Grid Construction: 11s and 13s: Polygonal Sub-Grid Construction using the Radii Matrix technique – Part One
  39. 39. Sub-Grid Construction: 11s and 13s: Polygonal Sub-Grid Construction using the Radii Matrix technique – Part Two
  40. 40. Sub-Grid Construction: 11s and 13s: Polygonal Sub-Grid Construction using the Radii Matrix technique – Part Three
  41. 41. Sub-Grid Construction: 11s and 13s: Polygonal Sub-Grid Construction using the Radii Matrix technique – Part Four
  42. 42. Completed Sub-Grid: 11s and 13s
  43. 43. Pattern Construction: 11s and 13s:
  44. 44. Pattern Construction: 11s and 13s:
  45. 45. Pattern Construction: 11s and 13s:
  46. 46. Pattern Construction: 11s and 13s:
  47. 47. Pattern Construction: 11s and 13s:
  48. 48. Pattern Construction: 11s and 13s:
  49. 49. Pattern Construction: 11s and 13s:
  50. 50. Pattern Construction: 11s and 13s:
  51. 51. Pattern Construction: 11s and 13s:
  52. 52. Pattern Construction: 11s and 13s:
  53. 53. Pattern Construction: 11s and 13s:
  54. 54. Pattern Construction: 11s and 13s:
  55. 55. Pattern Construction: 11s and 13s:
  56. 56. Pattern Construction: 11s and 13s:
  57. 57. Pattern Construction: 11s and 13s:
  58. 58. Pattern Construction: 11s and 13s:
  59. 59. Pattern Construction: 11s and 13s:
  60. 60. Pattern Construction: 11s and 13s:
  61. 61. Pattern Construction: 11s and 13s:
  62. 62. Pattern Construction: 11s and 13s:
  63. 63. Pattern Construction: 11s and 13s:
  64. 64. Pattern Construction: 11s and 13s:
  65. 65. Compound Pattern – 11s and 13s: Redrawn image of this exceptional Azerbaijani pattern
  66. 66. Allahu Akbar Thank You Jay Bonner Design Consultant Santa Fe, New Mexico USA Email: [email_address] Web Site: www.bonner-design.com

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