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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 Eratosthanes most famous for?
(a) He developed a way to navigate using logitude and latitude.
(b) He showed that there are no even prime numbers.
(c) He showed that the Earth must be a sphere.
(d) He developed a simple way to find prime numbers and for determining the circumference of the Earth.

2. Where did Hippocrates come from?
(a) Athens.
(b) Constinople.
(c) Rome.
(d) Chios.

3. Which of the following was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?
(a) Euclid constructed squares on the sides of right triangles.
(b) Euclid used his own axioms and propositions to show relationships,
(c) Euclid used propositions about similar angles and parallel lines.
(d) Euclid stated that the diagonal hypotenuse of a right triangle is equal to the sums of the squares of the two legs.

4. What is true about prime numbers?
(a) Prime numbers can never be an odd number.
(b) That for every group of prime numbers, there exists at least one more prime.
(c) Prime numbers can not exist in a finite series.
(d) Prime numbers are not divisible by other numbers.

5. Dunham showed that Heron's proof could also be used as which of the following?
(a) A proof of the Pythagorean Theorem.
(b) A proof of Archimedes' number theory.
(c) A proof of Euclid's number theory
(d) A proof of Hippocrates' squared areas.

Short Answer Questions

1. What did Apollonius work with in mathematics?

2. Who was the author of the book Elements?

3. Which of the following was an important proposition given by Euclid's number theory?

4. Which of the following is true in modern math about twin primes?

5. What name did Euclid give for numbers that could be divided by numbers other than themselves and one?

Short Essay Questions

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

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

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

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

5. Describe the contents of Cardano's book.

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

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

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

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

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

(see the answer keys)

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