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 I

Q 1. Give an example of a syllogism. Who introduced it and what was a motivation of this ?

Q 2. Which period is ”the Golden Age” of the ancient Greek mathematics ? Which mathematician belong to this age and when (approximately) did they live ? What was their main contribution to Mathematics ?

Q 3. What did Euclid mean by ”elements” ?

Q 4. What is the content of the Book I of ”Elements” and which results appear in the end of it ?

Q 5. Which titles can be found in the ”Elements”: Theorems, Propositions, Lemmas, Axioms, Postulates, Definitions, Common Notions, Special Notions, Preface, Acknowledgements, Remarks, Comments, Exercises, Problems, Conclusion.

Q 6. How many Books are in Euclid’s ”Elements” ? Which books are devoted to Geometry of the Plane, which ones to Number theory, and which ones to the three-dimensional solids ? Which books concern the results achieved by Pythagoras and his school ? Works of which other mathematicians are also presented in the ”Elemetns” ? In which Books ?

Q 7. Which angle is called ”obtuse” ?

Which triangle is called ”scalene” ?

How do we call triangles with two equal sides ?

What is an ”oblong” ?

Q 8. Give two examples of results in Number Theory from Euclid.

Q 9. What does mean Q.E.D. and Q.E.F. and in which situations these abbreviations were used ?

Q 10. What does mean ”consistency”, ”completeness” and ”independence” of an axiomatic system ? Who provided an axiomatic system of Geometry satisfying these conditions ?

Q 11. What is the approximation of number π by Archimedes ? How did he found it ?

Q 12. Sketch the spiral of Archimedes and give a formula for it.

Q 13. What is the Law of buoyancy ?

Q 14. What does mean ”the center of mass of a triangle” ? How to find it ?

Q 15. Which figure is engraved on the Tomb of Archimedes? Formulate the result of Archimedes it refers to.

Q 16. How the concept of a cone was modified by Apollonius ? Sketch how one can obtain different conic section depending on the position of the plane.