METU Department of Mathematics Math 303 History of Math Concepts Fall 2012

Final

January 4 2013, 17:40 – 19:20

Name and the student number:

Part I (18 questions, 40 points, 50 min)

Q1(2pts). Whose names are related to the Liar paradox, and when it was formulated ? Which other paradoxes (AFTER Zeno) do you know ?

Q2(2pts). What is the period of the first and the second Alexandrian schools ? Characterize the specific features of mathematics of these two periods.

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

Q4(2pts). What is the Heronian mean ? How it is used in a formula of volume (sketch a solid) ?

Q5(2pts). What are the names of the main books of Diophantus and of Pappus ? In which century did they work ?

Q6(2pts). What are ”diophantine equations” ?

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

Q8(2pts). How to construct geometrically point D which harmonically conjugate to a point C on interval AB ? Give a sketch.

Q9(2pts). In which century did Theon live, in which city ? What is he famous for ?

Q10(2pts). Who was the first woman-mathematician ? Write her name in Greek letters.

Q11(2pts). Which rational approximation of π was found by Chineese mathematicians ? When is happened, and what was the method ?

Q12(2pts). In which century zero as a number was introduced and commonly accepted in India ? What does mean “zero as a number” in compare with “zero as a sign” ?

Q13(3pts). 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 ? Till which time did it exist ?

Q15(3pts). When (approximately) did al-Khwarezmi live ? How the word ”algebra” is related to him ? What is the content of his main work ?

Q16(3pts). In which century did live Omar Khayyam and what is the content of his mathematical works ?

Q18(2pts). What are the three stages of development of algebraic notation ?

Q17(3pts). When did live al-Karaji and al-Kashi ? What they are famous for ?