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E-grāmata: Islamic Design: A Mathematical Approach

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This book deals with the genre of geometric design in the Islamic sphere. Part I presents an overview of Islamic history, its extraordinary spread from the Atlantic to the borders of China in its first century, its adoption of the cultural outlook of the older civilisations that it conquered (in the Middle East, Persia and Central Asia), including their philosophical and scientific achievements - from which it came to express its own unique and highly distinctive artistic and architectural forms. Part II represents the mathematical analysis of Islamic geometric designs.

The presentation offers unlimited precision that allows software to reconstruct the design vision of the original artist. This book will be of interest to Islamic academics, mathematicians as well as to artists & art students.

Recenzijas

I am delighted that a book like this, which offers substantial contributions to the literature has been published. It provides inspiration for others, including undergraduate mathematics students, who are seeking interdisciplinary topics for independent research. (Joel Haack, MAA Reviews, August 18, 2019)

Part I Cultural Context
1 A History
3(14)
1.1 The Revelations
3(1)
1.2 Early Conquests
4(1)
1.3 Islam and the Civilisations of the Ancient World
4(1)
1.4 The Umayyads and Damascus
5(1)
1.5 The Abbasids and Baghdad
5(1)
1.6 The Disintegration of the Caliphate
6(1)
1.7 The Sunni Revival
7(1)
1.8 The Mongol Cataclysm
8(2)
1.9 The Islamic Revanche: The Ilkhanids and Timurids
10(1)
1.10 The Early-Modern Islamic States
11(2)
1.11 Spain and the Maghreb
13(1)
1.12 Imperialist Encroachment and Islamic Decline
14(3)
2 The Scientific Contribution
17(8)
2.1 The Greek Connection
17(2)
2.2 The Pythagorean/Platonic Tradition
19(1)
2.3 Philosophy in Islam
20(1)
2.4 Religious Revival, Scientific Retreat
21(1)
2.5 Continuity and Transmutation
22(3)
3 The Religious Dimension
25(6)
3.1 `There Is No God but God'
25(1)
3.2 The Qur'an
26(1)
3.3 Traditions (Hadith)
27(1)
3.4 Islamic Identity and the Image Controversy
27(1)
3.5 Mizan, Symmetry and Cosmic Equilibrium
28(1)
3.6 The Islamic Paradise (al-Djanna)
29(2)
4 The Evolution of Style
31(10)
4.1 Consistency and Variety
31(1)
4.2 Symmetry and Geometry
32(2)
4.3 Earlier Islamic Art
34(1)
4.4 Baghdad, Samarra and Political Fragmentation; 8th-10th Centuries
34(1)
4.5 Stylistic Maturity; 11th-12th Centuries
35(1)
4.6 The Islamic Decorative Canon
36(1)
4.7 The Craft Group
37(1)
4.8 The Role of Paper in Islamic Art and Architecture
38(3)
5 Materials and Media
41(10)
5.1 Stonework
41(1)
5.2 Brickwork
42(1)
5.3 Ceramic Tiles and Ceramic Mosaic
43(2)
5.4 Stucco/Plasterwork
45(1)
5.5 Woodwork
45(2)
5.6 Book Illumination
47(1)
5.7 Court Patronage and Cottage Industry
48(3)
6 Countries and Regions
51(12)
6.1 Egypt
51(1)
6.2 India
51(2)
6.3 Iran
53(1)
6.4 Morocco
53(1)
6.5 Spain
54(1)
6.6 Syria
55(1)
6.7 Central Asia
56(2)
6.8 Turkey
58(5)
Part II Mathematical Analysis
7 Introduction
63(6)
7.1 Geometry
63(6)
7.1.1 Rosettes
64(5)
8 A Worked Example
69(6)
9 An Octagonal Set
75(12)
10 Octagonal Tiles with a Large Star
87(16)
10.1 16-Pointed Stars
87(6)
10.1.1 Adding Octagonal Tiles
88(5)
10.2 24-Pointed Stars
93(6)
10.3 A 32-Pointed Star
99(4)
11 Lines and Edges
103(14)
11.1 Strict Interlacing
105(4)
11.2 Borders
109(1)
11.3 Banding
109(3)
11.4 Irregular Borders
112(2)
11.5 Interlace Path Tracing
114(3)
12 Decagonal Patterns
117(12)
12.1 A Simple Tile Set
117(2)
12.2 Variable Diamond Patterns
119(2)
12.3 Fixed-Size Diamond Patterns
121(1)
12.4 Adding a 5-Pointed Star
121(3)
12.5 Another Simple Tile Set
124(4)
12.6 Some Erratic Patterns
128(1)
13 What Is Correct?
129(8)
13.1 An Example from the Alhambra
129(2)
13.2 Bourgoin Plate 32
131(1)
13.3 Bourgoin Plate 75
132(3)
13.4 An Egyptian Qur'an
135(1)
13.5 Conclusions
136(1)
14 6-Fold Delights
137(14)
14.1 Roman Influences
137(2)
14.2 Simple Islamic Designs
139(1)
14.3 Simple Islamic Designs Without Stars
139(1)
14.4 Simple Islamic Designs with a Single Rosette
140(2)
14.5 Designs with Two Rosettes
142(4)
14.6 Some More Complex Designs
146(1)
14.7 A Motif with Two Symmetries
147(4)
15 Two-Level Patterns
151(16)
15.1 An Iranian Example
151(1)
15.2 An Indian Example
152(1)
15.3 A Decagonal Example
153(2)
15.4 The Topkapi Scroll
155(2)
15.5 A Complex Issue to Resolve
157(3)
15.6 A Complex Pattern: Darb-I Imam Shrine
160(1)
15.7 A Complex Pattern: Seyyed Mosque
160(7)
16 Two Mamluk Masterpieces
167(16)
16.1 The Trigonometric Method
169(3)
16.2 The Manual Method
172(3)
16.3 A Comparison
175(2)
16.4 A Second Mamluk Masterpiece
177(6)
17 Conclusions
183(8)
17.1 Approximate Methods
183(1)
17.2 Ruler and Compass
184(1)
17.3 Use of Mathematics
185(1)
17.4 The Geometric Time-Line
186(2)
17.5 Pattern Type by Region
188(1)
17.6 A Summary of Methods
189(2)
17.6.1 Complete Analysis
190(1)
17.6.2 Incomplete Analysis
190(1)
Appendix A The Symmetry of a Tiling 191(20)
Appendix B Key Dates 211(2)
Appendix C Glossary 213(2)
Appendix D Copyright 215(2)
References 217(4)
Index 221
Brian Wichmann is the author of a CD/booklet published by World Scientific on geometric patterns. He obtained a DPhil (Oxon) in Mathematics, then had a career in software engineering research at NPL before starting a retirement project of collecting all known classical Islamic geometric patterns. The collection is at tilingsearch.org.

David Wade is the author of a number of books about Islamic Art and related topics. He is also responsible for the web site patterninislamicart.com which has over 4,000 photographs of patterns in Islamic Art. This is a major source of photographs for the book.