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. As described by Archimedes, what is always true about he diameter of the circle?
(a) It's never proportional to its circumference.
(b) It's equal to the square of the radius.
(c) It's always proportional to its circumference.
(d) It's equal to pi.

2. According to Euclid, when is a triangle a right triangle?
(a) When a triangle has three sides whose squares are equal to the area of the triangle.
(b) When a triangle does not have a side which can be considered a hypotenuse.
(c) When a triangle has a side whose square is the sum of the squares of the two legs.
(d) When a triangle can be constructed with three unequal sides.

3. What range of values did Archimedes determine for pi?
(a) Between 3 and 3 1/2.
(b) Between 3 and 4.
(c) Between 3 1/2 and 3 5/8.
(d) Between 3 10/11 and 3 1/7.

4. What was Hippocrates famous for?
(a) His ability to construct circles without a compass.
(b) His theorem on the quadrature of the lune.
(c) His proof on right triangles.
(d) His proof defining gravity.

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

Short Answer Questions

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

2. What did Hippocrates do that advanced mathematical methods?

3. Where did Hippocrates come from?

4. In what century did Archimedes live?

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

(see the answer key)

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