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

Midterm 2

December 10 2012, 17:40 – 19:00

Name and the student number:

Part I (16 questions, 31 points, 40 minutes)

Q1 (2pts). Which period is called “the Golden Age of the ancient Greek mathematics” ? Which mathematician of this period do you know ?

Q2 (2pts). What is the importance of Euclid’s “Elements” ? What did Euclid mean by ”elements” ?

Q3 (2pts). How many books are in the “Elements” ? Which subjects are covered there ? Which Books there are devoted to Geometry ?

Q4 (2pts). How an angle is called if it is greater that 90^{∘} ? How are called the triangles with two equal sides ? With three equal sides ? If all the sides are unequal ?

Q5 (2pts). Give examples of two important theorems in Number Theory from Euclid’s “Elements”.

Q6 (2pts). What does mean Q.E.D. and Q.E.F. and in which situations these abbreviations were used ?

Q7 (2pts). Which figure is engraved on the Tomb of Archimedes? Formulate the result of Archimedes it is related with.

Q8 (2pts). Which approximation of number π was found by Archimedes ? Which method did he use for that ?

Q9 (2pts). Sketch a spiral of Archimedes and give a formula for it.

Q10 (2pts). What was understood by a cone before Apollonius, and how did he modify this concept ? Sketch.

Q11 (2pts). Who introduced the polygonal numbers ? What are the first five triangular numbers ?

Q12 (2pts). What is the focal property of a parabola ? Who discovered it and in which book it is described ?

Q13 (1pt). Who introduced terms ”ellipse”, ”parabola”, and ”hyperbola” for the conic sections ?

Q14 (2pts). What is Eratosthenes famous for in Mathematics ? What were his other interests and achievements ?

Q15 (2pts). What is a conchoid and a cissoid ? Who introduced them and in which century ?

Q16 (2pts). Who is known as the greatest astronomer of antiquity ? When did he live and what are his achievements ?