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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. In general, what did Euclid's number theory describe?
(a) The relationship of fractions to decimals.
(b) The relationship of decimals to integers.
(c) The nature of whole numbers.
(d) The nature of measuring geometry.

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

3. Where was Archimedes born?
(a) Sicily.
(b) Rome.
(c) Olympia.
(d) Athens.

4. Which of the following were an example of twin primes?
(a) 2 and 6.
(b) 11 and 13.
(c) 19 and 22.
(d) 15 and 16.

5. That properties of specific shapes were early Egyptians aware of?
(a) Right triangles.
(b) Irregular solids.
(c) Parallelograms.
(d) Pi and the diameter of a circle.

Short Answer Questions

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

2. What was Eratosthanes most famous for?

3. What did Archimedes manage to prove using Euclid's ideas?

4. Exactly what limit is reached at a quartic equation?

5. What was the same about Apollonius and Erosthanes?

Short Essay Questions

1. Describe what Gauss discovered according to Dunham.

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

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

4. Describe what the Egyptians knew about geometry and triangles before Hippocrates.

5. Explain why Archimedes finding a number value for pi was considered a great achievement according to Dunham.

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

7. Describe how Cardano eventually publishes the solution to cubic equations.

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

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

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

(see the answer keys)

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