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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. "Straight lines in the same plane that will never meet if extended forever" is a definition of what?
(a) Intersection.
(b) Circle.
(c) Parallel lines.
(d) 180 degree angle.

2. 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 neither greater than nor less than the area of the triangle and therefore must be equal to it.
(d) He demonstrated that the area of the circle is always greater than the area of the triangle.

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

4. What was Hippocrates's great advance to mathematics?
(a) He showed how to square a circle.
(b) He showed how to square a figure with curved sides.
(c) He showed how to simplify the area of a triangle.
(d) He showed how to find the angles in a right triangle.

5. What was Euclid's definition of a prime number?
(a) Numbers which do not, and can not, contain a perfect number.
(b) Numbers which are divisible by 2.
(c) Numbers which contain an infinite number of composite numbers.
(d) Numbers which can only be divided by themselves and 1.

Short Answer Questions

1. Which of the following is an example of a perfect number?

2. Which of the following can not be solved using algebra?

3. What did Dunham claim about Archimedes's determination of a number value for pi?

4. Where was Neil's Abel from?

5. Which mathematician was first to take the challenge to solve cubic equations?

Short Essay Questions

1. What was Euclid's definition of composite and perfect numbers?

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

3. Summarize, in a sentence, what was Hippocates's great theorem, and what was it based on according to Dunham?

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

5. Explain when the knowledge of ancient scholars was rediscovered.

6. Describe Euclid's definition of prime numbers and the relationship he stated as existing between prime and composite numbers.

7. Describe what is quadrature and why it was useful in the time of Hippocrates.

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

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

10. How many definitions were in Euclid's book? List some of the definitions he included.

(see the answer keys)

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