Journey Through Genius: The Great Theorems of Mathematics Quiz | Eight Week Quiz B

William Dunham (mathematician)
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This quiz consists of 5 multiple choice and 5 short answer questions through Euclid and the Infinitude of Primes.

Multiple Choice Questions

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

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

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

4. How did Lindeman prove his conclusion?
(a) Lindeman proved that some numbers are constructable without the use of a compass.
(b) Lindeman proved that all numbers are constructable with a compass and ruler.
(c) Lindeman proved that some numbers are not constructable with only a compass and straight-edge.
(d) Lindeman proved that square roots are irrational numbers.

5. What did the Pythagorean Theorem accomplish for mathematics?
(a) The ability to find square roots.
(b) The concept of providing a logical proof.
(c) The concept of constructing useful mathematics.
(d) The ability to measure angles.

Short Answer Questions

1. Which of the following is an example of a postulate that must be accepted in Elements?

2. Numbers whose divisor add up to itself, was considered which type of number according to Euclid?

3. Which of the following was NOT one of Gauss' discoveries?

4. Which of the following could NOT be included as a step in Euclid's great theorem?

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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