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

Midterm 1

November 8 2012, 17:40 – 19:00

Name and the student number:

Part II

Q 1. What does mean “incommensurable magnitudes” ?

Q 2. How do you understand expression “geometric algebra” ?

Q 3. For the following scientists describe their contribution to mathematics that you know

(1) Eudoxus of Cnidus

(2) Theaetetus

(3) Zeno of Elea

(4) Hippocrates of Chios

(5) Hippias of Elis

(6) Aristotle Q 4. Give a formula for the Pythagorian triples of integers a, b, c, such that a^{2} + b^{2} = c^{2}. How does it look like in the special case of c = a + 1 ?

Q 5. What are the perfect numbers ? Give Euclid’s formula for such numbers and use it to find the first four perfect numbers.

Q 6. What is the Golden Ratio and how it is related to the Pentagram ?

Q 7. Sketch a proof that the square root of 2 is irrational.

Q 8. What are the four Means that were known to Pythagoras ? Give a formula (for two numbers) and compare them.