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This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.

Multiple Choice Questions

1. Which of the following best describes Archimedes as discussed by Dunham?
(a) Absent-minded genius.
(b) Loud and arrogant.
(c) Creative but stubborn.
(d) Mild-mannered researcher.

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

3. What name did Euclid give for numbers that could be divided by numbers other than themselves and one?
(a) Even numbers.
(b) Perfect numbers.
(c) Composite numbers.
(d) Discrete numbers.

4. What instruments did the Greeks use to square a shape?
(a) A pendulum.
(b) A small grid.
(c) A compass and a ruled straight-edge.
(d) A sphere and ruler.

5. What did Gauss set out to prove?
(a) That the sum of the angles in a triangle is 180 degrees.
(b) That a right angle is always equal to 90 degrees.
(c) That a circle can have less than 360 degrees.
(d) That Euclid's postulate on straight lines was incorrect.

Short Answer Questions

1. What did Plato use his inspiration from Euclid for?

2. In what century did Archimedes live?

3. How many definitions were stated in Elements?

4. Which of the following is an example of a postulate that must be accepted in Elements?

5. What is a "depressed cubic"?

Short Essay Questions

1. Describe the events that follow del Ferro's death between Fior and Tartaglia.

2. Describe what work of Euclid's fascinated Plato and his theory on the shape of the Universe.

3. Who was Luca Pacioli, and what controversy was sparked over his writings?

4. Explain in two sentences Euclid's method to prove the Pythagorean Theorem.

5. Describe Lindeman's work on the square of a circle, and state what he discovered.

6. Describe Euclid's postulates and notions in how they were important in constructing his proofs.

7. What did Dunham claim was Pythagoras's major contribution to geometry, and mathematical reasoning?

8. According the Dunham, how did Euclid prove his theory on the infinitude of primes?

9. How did Heron find the area of a triangle, and what did Dunham state about Heron's work?

10. Explain who was Hippocrates, his contribution to mathematics, and how do we know about him?

(see the answer keys)

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