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

Midterm 2

December 9 2010, 17:30 – 19:00

Name and the student number:

Part II

Q 1. How did Euclid (following Eudoxus) defined that magnitudes a and b are in the same ratio as magnitudes c and d ?

Q 2. Describe (in your own words) the fifth Postulate from ”Elements”.

Q 3. What does mean ”Geometric Algebra” ? Give an example illustrating this idea.

Q 4. According to Pruclus, every problem and every theorem should contain the following elements:

(1) an enunciation

(2) an exposition (or setting out)

(3) a specification (or definition of goal)

(4) a construction

(5) a proof

(6) a conclusion Below is the enunciation of Proposition I.6 of Euclid’s ”Elements”:

If in a triangle two angles be equal to one another, the sides which subtend the equal angles be also equal one another.

Supply the remaining part of this theorem (in your own words, not necessarily Euclid’s).

Q 5. Formulate the results of Archimedes concerning quadrature of a sector of parabola.

Q 6. What is a semiregular polyhedron ? Who enumerated them and what is their number ? How to obtain such a polyhedron by truncation of an octahedron ? Which polygons are the faces of such a truncated octahedron and what is their number ?