Table of contents

Islamic Geometric Ornaments in Istanbul

  1. Preface ………. 3
  2. Introduction  ………. 5
  3. A glimpse into the past  ………. 8
  4. Where is mathematics?  ………. 13
  5. A simple example  ………. 20
  6. Regular polygons  ………. 25
    1. On an equilateral triangle, regular hexagon and regular dodecagon ……….. 27
    2. Construction of an equilateral triangle from a segment  ………. 28
    3. Construction of a regular hexagon from a segment  ………. 28
    4. Construction of an equilateral triangle inscribed in a circle  ………. 29
    5. Construction of a regular hexagon inscribed in a circle  ………. 29
    6. Construction of a regular dodecagon inscribed in a circle ………. 30
    7. On a square, an octagon and hexadecagon ……… 32
    8. Construction of a square with a given side ……… 32
    9. Construction of a regular octagon with a given side ……. 32
    10. Construction of a square inscribed in a circle ………. 33
    11. Construction of a hexadecagon inscribed in a circle ………. 33
    12. On a regular pentagon and a regular decagon ……… 34
    13. Construction of a regular pentagon inscribed in a circle ………. 35
    14. Construction of a regular decagon inscribed in a circle ……… 36
    15. On some odd sided regular polygons ………. 37
    16. Construction of a regular heptagon ………. 37
    17. Construction of a regular enneagon ………. 38
    18. Construction of a regular hendecagon inscribed in a circle ……… 40
  7. In the labyrinth of grids and stars ………. 41
  8. Construction of a double star ornament ………. 45
  9. A tour through Istanbul ……… 48
    1. Walk 1: The Sultan Ahmed Mosque ……… 48
    2. Walk 2: The Great Hagia Sophia ……… 63
    3. Walk 3: The Şehzade Mosque or the Prince’s Mosque …….. 70
    4. Walk 4: The tomb of Mahmut Paşa …….. 85
    5. Walk 5: Some hidden treasures ……… 90
  10. Where to go from here? ……… 109
  11. Appendix: Sketchpad and geometric ornament design ………. 115
    1. Custom tools in Sketchpad ………. 115
    2. A few hints on using Sketchpad in creating geometric ornaments …….. 118
  12. Literature ………. 120
  13. Internet Resources ………. 120
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