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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. As described by Dunham, what did Archimedes demonstrate first in his proof on pi?
(a) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's hypotenuse and the other leg equal to the circle's circumference.
(b) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's diameter.
(c) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's circumference.
(d) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's diameter and the other leg equal to the circle's circumference.

2. Which of the following was an important proposition given by Euclid's number theory?
(a) Numbers from one to ten are only divisible by composite numbers.
(b) Any even number is divisible by 3.
(c) Any perfect number is divisible by some composite number.
(d) Any composite number is divisible by some prime number.

3. What does the Pythagorean Theorem state?
(a) For any triangle the sqaured sum of the legs is equal to half the hypotenuse.
(b) For any triangle the sum of the legs squared is equal to the length of the hypotenuse.
(c) For any right triangle the diagonal side is equal to the sum of the legs.
(d) For any right triangle the square of the diagonal side is equal to the sum of the squares of the two legs.

4. In Elements, how many postulates must be accepted as given?
(a) Five.
(b) Twelve,
(c) Eighteen.
(d) Twenty-two.

5. What was the title of Cardano's book which contained the solution to the cubic?
(a) La Magnifica.
(b) Ars Magna.
(c) Tarsisia.
(d) Elements.

Short Answer Questions

1. What did Hippocrates do that advanced mathematical methods?

2. Who was Heron?

3. What did Euclid do in his 48th proposition?

4. Dunham showed that Heron's proof could also be used as which of the following?

5. In general, what did Euclid's number theory describe?

Short Essay Questions

1. What did Euclid state for his theory on prime numbers?

2. What did Dunham describe in the epilogue of the chapter?

3. Describe the ancient city Alexandria and name a few of its third century geniuses.

4. What did Dunham explain about the shift in learning from the West to the East?

5. Describe why Dunham infers that Euclid's Elements was an evolutionary book not so much for what it said, but in how it was presented.

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

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

8. What was already known about circles before Archimedes?

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

10. Explain what Neils Abel proved.

(see the answer keys)

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