Chapter 9: The Mathematics of Islam

1. When did the Islamic civilization originate?

2. Many of the manuscripts in the Baghdad library originated from where?

3. What happened to mathematical development in Islam starting in the eleventh century?

4. Why is this chapter called "The Mathematics of Islam" rather than "Arabic Mathematics"?

5. From where does the word "algorithm" derive?

6. What algorithms did al-Khwarizmi include in his arithmetic text? How did he write fractions?

7. How did al-Uqlidisi's arithmetic text innovate beyond al-Khwarizmi's text?

8. How was the development of decimal fractions furthered by al-Samaw'al, and then al-Kashi?

9. How did Islamic scholars prove algebraic facts?

10. What are "al-jabr" and "al-muqabala"? Which of these terms became the name of this science?

11. Why was a sixfold classification of quadratic equations necessary? Does the classification actually include all possible quadratic equations?

12. Create (and explain) a geometric justification for the solution of the equation "What must be the square which, when increased by six of its own roots, amounts to ninety-one?"

13. To what extent does al-Khwarizmi abide by the promise in the preface of his text, to write about what is "useful"?

14. How did Abu Kamil's treatment of "number" and "magnitude" differ from the Greek concept, and begin to pave the way towards a new understanding of the concept of "number"?

15. What were the contributions of al-Karaji to Algebra?

16. What were the contributions of al-Samaw'al to Algebra?

17. In what context does the concept of "proof by induction" first appear in Islamic mathematics?

18. To what extent was al-Khayyami able to solve cubic equations algebraically?

19. Verify that 220 and 284 are amicable numbers.

20. To what extent was al-Khwarizmi influenced by Greek mathematics? 21. What value did al-Khwarizmi use for pi?

22. Under what conditions were Islamic mathematicians able to prove Euclid's parallel postulate?

23. For what reasons were Islamic mathematicians particularly interested in spherical trigonometry?

24. To what level of accuracy was al-Kashi able to calculate the sine of one degree?

25. In what way was Islamic mathematics a central factor to the revival of mathematical activity in Europe?

Exercises: # 2, 6, 22.