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

2. Which was true of Euclid's number theory?
(a) It was proven to the true by Hippocrates.
(b) It was incorrect, as proved by Plato.
(c) It has an impact on modern math.
(d) It has been proven too basic to be useful.

3. What did Dunham claim about Archimedes's determination of a number value for pi?
(a) Archimedes's number was very good, considering he did not have a way to calculate square roots.
(b) Archimedes's number was perfectly correct.
(c) Archimedes's number was not very accurate, considering the technology of his time.
(d) Archimedes's number could have been better if he had understood Euclid's work better,

4. Who was del Ferro's student?
(a) Antonio Fior.
(b) Gerolamo Cardano.
(c) Luca Pacioli.
(d) Niccolo Fontana.

5. Which of the following best describes Cardano's character?
(a) Flirtacious.
(b) Eccentric.
(c) Arrogant.
(d) Religious.

Short Answer Questions

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

2. Numbers whose divisor add up to itself, was considered which type of number according to Euclid?

3. Which of the following was NOT one of Gauss' discoveries?

4. What did most of Heron's work deal with?

5. Which of the following were an example of twin primes?

Short Essay Questions

1. Explain who was Gerolamo Cardano, and how did he become involved with the solution to the cubic.

2. Describe in two sentences Archimedes's method for determining circular area.

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

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

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

6. Describe who was Archimedes and how Dunham described his character.

7. Describe what Gauss discovered according to Dunham.

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

9. Who was Heron, and what is known about him today?

10. How did Archimedes find a number value for pi?

(see the answer keys)

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