Journey Through Genius: The Great Theorems of Mathematics Quiz | Four Week Quiz A

William Dunham (mathematician)
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This quiz consists of 5 multiple choice and 5 short answer questions through Archimedes' Determination of Circular Area.

Multiple Choice Questions

1. What was true about Hippocrates's proof?
(a) The proof was easy if their was advanced technology available.
(b) It was fairly easy and simple.
(c) The proof was exceedingly difficult and not understood at the time.
(d) It was useful for circles.

2. Which of Euclid's postulates troubled many of the following generations of mathematicians?
(a) Euclid's postulate on right triangles.
(b) Euclid's proof on right triangles.
(c) Euclid's postulate on creating an arc.
(d) Euclid's postulate on parallel lines.

3. What was Euclid's definition of a prime number?
(a) Numbers which do not, and can not, contain a perfect number.
(b) Numbers which are divisible by 2.
(c) Numbers which can only be divided by themselves and 1.
(d) Numbers which contain an infinite number of composite numbers.

4. 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.

5. 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 very good, considering he did not have a way to calculate square roots.
(d) Archimedes's number was not very accurate, considering the technology of his time.

Short Answer Questions

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

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

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

4. How did Lindeman prove his conclusion?

5. Which of the following was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?

(see the answer key)

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