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This quiz consists of 5 multiple choice and 5 short answer questions through A Sampler of Euler's Number Theory.

Multiple Choice Questions

1. Which words best describe how solid proofs were developed in Elements?
(a) Programmed order.
(b) Axiomatic framework.
(c) Inverted scaffold.
(d) Simple arguments.

2. What did Dunham discuss for many pages in this chapter?
(a) Heron's complicated proof.
(b) Heron's political tendancy.
(c) Heron's origins of the universe.
(d) Heron's religious beliefs-

3. Which city was the center of thinking and learning in Third century BC?
(a) Athens.
(b) Rome.
(c) Olympia.
(d) Alexandria.

4. What did Dunham claim about Archimedes's determination of a number value for pi?
(a) Archimedes's number could have been better if he had understood Euclid's work better,
(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 was very good, considering he did not have a way to calculate square roots.

5. What did Euler prove about 2²ⁿ + 1?
(a) That the statment is sometimes prime and sometimes composite.
(b) That the statement is always a composite number.
(c) That the statement is neither prime nor composite.
(d) That the statement is always a prime number.

Short Answer Questions

1. Where was the modern number system developed?

2. Which of Euclid's postulates troubled many of the following generations of mathematicians?

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

4. What did Dunham consider as Archimedes's "masterpiece"?

5. According to Euclid, when is a triangle a right triangle?

(see the answer key)

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