1. The Islamic conquests, and the Islamic world

2. Outline of Islamic history, with a few mathematicians.
622 ‘Hijra’. Flight of Muhammad to Medina. Beginning of Muslim era.
632. Death of Muhammad.
7th century. Conquests of Middle East, North Africa and Spain.
750. Abbasid dynasty established (based at Baghdad)
800. Khalif al-Ma’mun founds ‘House of Wisdom’ at Baghdad.
First mathematicians; translations, works on algebra, Indian numbers etc.
Al-Khwarizmi, Thabit ibn Qurra, Abu-l-Wafa
10th century. Break-up of Abbasid rule.
Al-Uqlidisi (Damascus), Abu Kamil (c.950), Al-Biruni (Iran) (c.1000)
11th-13th centuries. Crusades in Syria/Palestine.
11th century. Umar al-Khayyami (Iran), Al-Samaw’al.
13th century. Mongol conquest of Baghdad.
Nasir al-Din al-Tusi.
15th century. Ulugh Beg, Al-Kashi (Samarkand).

3. An Islamic manuscript (Al-Uqlidisi, 950)

4. Islamic mathematics

5. Constructing a heptagon. If BW=WG=GD=DA, and the angles
ADG, ABD are equal, then angle ADB=BAD=3.ABD; and so
angle ABD=2π/7.
However, the ratios of lengths AG, GB have to be fixed so that the relations of angles above work. This leads to a cubic equation, as al-Sijzi discovered. (10th century)

6. Astronomical table; 18th century copy of a 15th century original (Ulugh Beg)

7. Diagram: eclipse of the moon, by al-Biruni, about 1000 CE, Iran.

8. Table (al-Samaw’al) dealing with the division of two large polynomials.

9. Geometry in the design of arches (Al-Kashi, 15th century)

10. How artisans use geometry: approximate formulae to get patterns
How artisans use geometry: approximate formulae to get patterns. (From Daud
Sutton, Islamic Design, p. 45.)

11. A muqarna (geometric/architectural drawing) with, among other things,
a seven-pointed star and several five-pointed ones (From Gülru Necipoglu,
Topkapi manuscript)

12. Part of a ‘muqarna’ (vault) showing geometrical pattern

13. The ground plan of a muqarna, showing its geometry.