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. Which of the following is true about pi, as described by Dunham.
(a) The measurement of pi is no longer a mystery as we have an exact number value in modern mathematics.
(b) The measurement of pi is a challenge that continues into modern mathematics.
(c) The measurement of pi was redetermined after Archimedes's death.
(d) The measurement of pi should not have been so difficult for Archimedes to demonstrate.

2. What instruments did the Greeks use to square a shape?
(a) A sphere and ruler.
(b) A compass and a ruled straight-edge.
(c) A pendulum.
(d) A small grid.

3. What were the proofs in Elements based on?
(a) Lindeman's method.
(b) Basic definitions.
(c) Ancient greek geometry.
(d) Novel notions.

4. Which of the following is an example of a perfect number?
(a) 20.
(b) 6.
(c) 1.
(d) 10.

5. After working on pi, what did Archimedes continue with in his study of mathematics?
(a) He studied the volume to surface area ratios of cubes.
(b) He studied the relationship between ratios in triangles.
(c) He studied the relationship of sine to cosine.
(d) He studied the volume and surface area of spheres, cones, and cylinders.

Short Answer Questions

1. Which of the following best describes Archimedes as discussed by Dunham?

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

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

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

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

(see the answer key)

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