METU Department of Mathematics Math 303 History of Math Concepts Fall 2010

Final

January 8 2011, 14:30 – 16:30

Name and the student number:

Part I

Q1(2pts). Formulate the Appolonius Problem. Give a sketch.

Q2(2pts). Which period is called ”hellenistic” ? What is the period of the first and the second Alexandrian schools ?

Q3(2pts). Who did write ”Almagest”, what is it about, and what is its importance ? Which kind of mathematics does it develop ?

Q4(2pts). When (approximately) did Hero (Heron) live ? What is the Heronian mean ?

Q5(2pts). What is the title of the book of Nicomachus ? What was special about it, and why it raised criticism from mathematicians ?

Q6(2pts). How did Diophantus expanded the concept of a number? What are the ”diophantine equations” ?

Q7(2pts). Formulate the ”Last Fermat Theorem”. How it is related to Fermat ?

Q8(2pts). What is the name of the main work of Pappus ? When (approximately) it was written ?

Q9(2pts). How to calculate the cross ratio (a, b; c, d) ? How to construct geometrically point D which yields a ”harmonic division” of three points A, B, C on a line ? Give a sketch.

Q10(2pts). In which century did Theon of Alexandria live ? How his name is related to Euclid’s ”Elements” ?

Q11(4pts). What is the name of the most famous Chinese classical mathematical work ? What is its content ? Why it is sometimes compared with Euclid’s ”Elements”: what is similar and what is different ?

Q12(2pts). How would Chinese write (with Rod numbers) 125, and 308 ?

Q13(4pts). Which contribution to mathematics are Indians famous for ? When (approximately) did live Ariabhata and Brahmagupta ? What can you say about their works ?

Q14(2pts). What was the name of the Academy of Science in Baghdad ? In which century it was established ? For how long did it exist ?

Q15(2pts). When (approximately) did al-Khwarezmi live ? What is he famous for ?

Q16(2pts). What is the mathematical contribution of Omar Khayyam ?

Q17(2pts). What is the contribution of al-Kashi ?

Q18(2pts). When did Fibonacci live and what are the titles of his books ? What is their principal content ?