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 II (7 questions, 39 points, 50 min)

Q1(7pts). In which ratio does point 5 divides interval [1, 4] ? Which point is harmonically conjugate to 5 ? Find the cross ratio (1, 4; 2, 6).

Q2(7pts). Formulate the Pappus centroid theorems for calculation of the surface area and volume. Apply it in the case of torus.

Q3(6pts). 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 in its style and approach ?

Q4(8pts). Formulate the Chinese Remainder Theorem. in general. Find an integer n which gives 1 modulo 3, 4 modulo 5, and 5 modulo 8 (give the details of solution, not only the answer).

Q5(3pts). Apply Brahmaputra’s formula to find the area of a quadrilateral inscribed in a circle with the sides of length 5,6,7,8.

Q6(3pts). Formulate Brahmaputra’s Theorem (give a sketch).

Q7(6pts). Describe the approach of al-Tusi to solution of the cubic equation. What is the discriminant of a cubic equation and what does it describe ?