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

Midterm 1

November 4 2010, 17:40 – 19:00

Name and the student number:

Part II

Q 1. How would record number 26 (1) Babylonians

(2) Egyptians

(3) Maya

(4) Greeks in the alphabetical numeral system ?

(5) Greeks in the acrophonic numeral system ?

Q 2. What is the difference between place-value and sign-value numeral systems ? How can be characterized in that sense the numeral systems of Egyptians, Babylonians, Maya, and Romans ? What is the base of the above numeral systems ?

Q 3. What are the Pythagorian triples ? Give a formula for them.

Q 4. What are the perfect numbers ? Which kind of formula for them was discovered ?

Q 5. What is the Golden Ratio and how it is related to the Pentagram ? Prove this relation.

Q 6. Describe how using a compass and a straightedge one can bisect (1) an angle,

(2) a line segment.

Q 7. Give the names and formulations of the three great problems of Antiquity. What is the fourth problem that sometimes added to this list ?

Q 8. What is the importance of a Hippocratic Lunes ? Give an example and explain what is its area.