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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. Which is one of the common notions presented in Elements?
(a) "The inverse of a line makes a circle."
(b) "Things with are equal have an inverse that is equal."
(c) "Points with equal values can be connected with a line of equal value."
(d) "Things which are equal to the same thing are also equal to each other."

2. Which of the following is false about the modern implications of Euclid's number theory?
(a) Euclid gave a good idea for how to construct even perfect numbers.
(b) Whether there are no odd perfect numbers is still not known.
(c) Great mathematicians continue to puzzle over some aspects of Euclid's number theory.
(d) Euclid's recipe for constructing even perfect numbers is incorrect.

3. According to Dunham, who was most able to collect knowledge from around the globe?
(a) Roman emporers.
(b) Greek philosophers.
(c) Arabian scholars.
(d) Greek tradesman.

4. What name did Euclid give for numbers that could be divided by numbers other than themselves and one?
(a) Composite numbers.
(b) Perfect numbers.
(c) Even numbers.
(d) Discrete numbers.

5. Who was Eratosthanes?
(a) He was a mathematician, and leading doctor.
(b) He was the first to study political sciences.
(c) He was a teacher and philosopher.
(d) He was the chief librarian, and a mathematician.

Short Answer Questions

1. What did Dunham discuss for many pages in this chapter?

2. As described by Dunham, what did Archimedes demonstrate first in his proof on pi?

3. In what century did Archimedes live?

4. What was the same about Apollonius and Erosthanes?

5. Who was Heron?

Short Essay Questions

1. Explain some puzzles suggested by Euclid's theories.

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

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

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

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

6. Describe what Gauss discovered according to Dunham.

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

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

9. Explain what Neils Abel proved.

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

(see the answer keys)

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