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

William Dunham (mathematician)
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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. How did Archimedes arrive at a number value for pi?
(a) By proving that pi could not be a negative number.
(b) By constructing multi-sided polygons inside and outside a circle and determining their perimeters.
(c) By proving pi could not be equal to one.
(d) By constructing successively smaller circles inside circles until he realized all of their ratios of diameter to area were equal.

2. As described by Dunham, what did Archimedes demonstrate first in his proof on pi?
(a) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's diameter.
(b) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's diameter and the other leg equal to the circle's circumference.
(c) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's circumference.
(d) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's hypotenuse and the other leg equal to the circle's circumference.

3. Exactly what limit is reached at a quartic equation?
(a) The limit of algebra.
(b) The limit of logical geometric proofs.
(c) The limit of the decompressed cubic method.
(d) The limit of the Pythagorean Theorem.

4. Who acted as the gate keepers of knowledge?
(a) Greek philosophers.
(b) Arabian scholars.
(c) Roman emporers.
(d) Greek tradesman.

5. What was true about Heron's theorem as described by Dunham?
(a) It was to determine the area of a circle by measuring a right triangle inside the circle.
(b) It was to determine the volume of a sphere without measuring the circumference.
(c) It was to find the area of a triangle when only the length of the sides are known.
(d) It was to solve equations were only two varibles are known.

Short Answer Questions

1. Which of the following is INCORRECT, and not used in Archimedes proof of his theory?

2. What did Euclid do in his 48th proposition?

3. Which of the following can not be solved using algebra?

4. Where did Hippocrates come from?

5. What did most of Heron's work deal with?

(see the answer key)

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