View a FREE sample

This test consists of 15 multiple choice questions and 5 short answer questions.

Multiple Choice Questions

1. What was most useful about finding the square of a shape, before Hippocrates?
(a) It was useful in finding the area of oddly shaped pieces of land.
(b) It was useful in finding the area of circles.
(c) It was useful in creating simple elevation maps,
(d) It was useful in determining the distance between two points.

2. What did Dunham consider extraordinary about the Elements?
(a) How Hippocrates ordered the book.
(b) The content was not based on previous authors' work.
(c) The content was totally unique.
(d) How geometric proofs were presented.

3. Which of the following is false about the modern implications of Euclid's number theory?
(a) Euclid's recipe for constructing even perfect numbers is incorrect.
(b) Euclid gave a good idea for how to construct even perfect numbers.
(c) Whether there are no odd perfect numbers is still not known.
(d) Great mathematicians continue to puzzle over some aspects of Euclid's number theory.

4. How did Archimedes demonstrate his theory of pi?
(a) He demonstrated that the area of the circle is never equal to the area of the triangle.
(b) He demonstrated that the area of the circle is never less than the area of the triangle.
(c) He demonstrated that the area of the circle is always greater than the area of the triangle.
(d) He demonstrated that the area of the circle is neither greater than nor less than the area of the triangle and therefore must be equal to it.

5. Which of the following was NOT defined by Euclid?
(a) Even numbers.
(b) Whole numbers.
(c) Nominal numbers.
(d) Odd numbers.

6. Which of the following is an example of a perfect number?
(a) 6.
(b) 1.
(c) 10.
(d) 20.

7. In what century did Archimedes live?
(a) First century A.D,
(b) Twelthf century A.D.
(c) Nineteeth century A.D.
(d) Third century B.C.

8. What were the proofs in Elements based on?
(a) Lindeman's method.
(b) Basic definitions.
(c) Ancient greek geometry.
(d) Novel notions.

9. Which mathematician was first to take the challenge to solve cubic equations?
(a) Luca Pacioli.
(b) Scipione del Ferro.
(c) Niccolo Fontana.
(d) Tartaglia.

10. How many sides did the pentadecagon have, as presented by Euclid?
(a) Fifteen.
(b) Twenty.
(c) Five.
(d) Ten.

11. What shape was NOT demonstrated in the Elements as having a relationship to other shapes?
(a) Hyperbola.
(b) Pentagon.
(c) Hexagon.
(d) Triangle.

12. Who was the author of the book Elements?
(a) Hippocrates.
(b) Lindemann.
(c) Einstein.
(d) Euclid.

13. What did Ferdinand Lindeman prove in 1882?
(a) That the square root of the hypotenuse of a right triangle can not be found.
(b) It is impossible to find the square of a semicircle.
(c) That the square of a circle can not be found with a compass and a straight-edge.
(d) It is possible to find the square of a circle.

14. Which of the following was true about Cardano, according to Dunham?
(a) He was jailed for heresy.
(b) He was a priest.
(c) He was not a mathematician.
(d) He had three wives.

15. Which of the following was one of Euclid's great theorems?
(a) There exists an infinite number of prime numbers.
(b) Prime numbers are more comples than discrete numbers.
(c) There exists only infinite and whole numbers.
(d) There exists an finite number of prime numbers.

Short Answer Questions

1. What was the bases of Hippocrates's proof ?

2. What was true about Hippocrates's proof?

3. What did Dunham consider as Archimedes's "masterpiece"?

4. What was Hippocrates's great advance to mathematics?

5. After Hippocrates, what shape did the Greeks attempt to square without success?

(see the answer keys)

This section contains 653 words (approx. 3 pages at 300 words per page) View a FREE sample