1. The Rise of Islamic Mathematics
8th – 13th Century

2. 622 A.D. Mohammed escapes from Mecca to Medina
The day he arrives at Yathrib El Medinat (Medina) is the beginning of the new year in the Islamic Calendar
Returned to Mecca a hero and unites the scattered tribes

3. Arab-Islamic Expansion
India
Persia
Mesopotamia
Northern Africa
Spain

4. Arab-Islamic Expansion
Caliph – An Islamic leader acting in Mohammed’s place after his death in 632 AD
Eastern Caliph – reigned in Baghdad
Western Caliph – reigned in Cordoba

5. Preservation of Culture of Conquered Territories
“Cubic Equations and Intersections of Conic Sections” by Diophantus translated to Arabic kept in Tehran University
Arabs seized upon Greek and Hindu Erudition
Invited distinguished scholars to their courts
Translated Hindu and Greek works in
Astronomy
Medicine
Mathematics
Saved until Europe scholars came out of Dark Ages

6. The House of Wisdom Established by caliph al - Rashid
Primarily a Library
When his son had a dream of Aristotle, he made translating Greeks texts his goal
Place for Translation and Research
Scholars would work here in translating Greek and Hindu treatises to Arabic

7. 786 AD caliph Harun al-Rashid 809 AD caliph al Mâmûn
766 AD caliph al-Mansûr
Brahmagupta’s works brought to Baghdad
Hindu Numerals brought into Arabic mathematics
786 AD caliph Harun al-Rashid
Euclid’s Elements translated
809 AD caliph al Mâmûn
An observatory was built
Measured Earth’s meridian
Translated mathematical and astronomical work Almagest

8. Thabit Ibn Qurra: AD
Physician, Philosopher, Linguist, Mathematician
Best Translations
Ptolemy
Appollonius
Archimedes
Theodosius
Euclid

9. Abu’l Wefa: 940 – 998 AD Born in Persian Mountain Region of Khorasan
Translated Diophanthus
Father of Algebra
First solution of Cubic Equations
Found Rational Solutions to Curves
Perfected Ptolemy’s method of computing sine to nine decimal places

10. Ciphered System (like Ionic Greek)
10th and 11th Century and before 7th century:
Arabians wrote all numbers in words
Extensive Conquering:
Introduction of short symbolism
Ciphered System (like Ionic Greek)
Adopted Hindu Notation adopted by merchants
Hindu numerals excluded in Eastern Empire
Arabic Numeral System

11. Al-Khowarizimi: 800-847 AD Rules for Computing
Modeled after Hindu Algorithms
Casting out 9’s
False Position
Double False Position
Rule of Three
CASTING OUT NINE’S

12. Al-Khowarizimi Popularized number zero Algebra
Used geometry to prove algebraic results
Worked in astronomy

13. Al-Khowarizimi Wrote a treatise on Hindu-Arabic numerals
Introduced number zero
Introduced Hindu concept of decimal positioning

14. Al-Khowarizimi Wrote treatise entitled Kitab al-jabr wa’l-muqabalah
Practical application of algebra to Islamic Inheritance Laws
Al-jabr means “restoration” or “completion”
Al-muqabalah means “balancing”

15. Completing the Square

16. Completing the Square

17. Completing the Square

18. Completing the Square

19. Completing the Square

20. Ibrahim ibn Sinan – grandson of Thabit ibn Qurra

21. Ibrahim ibn Sinan – grandson of Thabit ibn Qurra

22. Ibrahim ibn Sinan – grandson of Thabit ibn Qurra

23. Ibrahim ibn Sinan – grandson of Thabit ibn Qurra

24. Ibrahim ibn Sinan – grandson of Thabit ibn Qurra

25. Ibrahim ibn Sinan – grandson of Thabit ibn Qurra

26. Geometry in Art

27. Abu Nasr al-Farabi: 900 -900 AD

28. Abu Nasr al-Farabi: 900 -900 AD

29. Abu Nasr al-Farabi: 900 -900 AD

38. Alhambra of Granada, Spain

39. Alhambra Symmetrical Patterns