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

William Dunham (mathematician)
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This quiz consists of 5 multiple choice and 5 short answer questions through Heron's Formula for Triangular Area.

Multiple Choice Questions

1. What was known about pi, during Archimedes' time?
(a) That is was the relationship between the diameter and circumference of a circle.
(b) Nothing, the concept of pi was unknown.
(c) That it was never the same number value for a given circle.
(d) That it could not be assigned a relationship between measurements in a circle.

2. What was the bases of Hippocrates's proof ?
(a) Properties of points and lines.
(b) Properties of triangles and semicircles.
(c) Properties of squares and cubes.
(d) Properties of area to volume measurements.

3. What did Heron's advances put into historical perspective for Dunham?
(a) A shift in learning across continents.
(b) A change in political theory across the globe.
(c) A shift in information flow that ignored socioeconomic order.
(d) A change in learning foundations in the ancient scholarly universities.

4. 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 volume and surface area of spheres, cones, and cylinders.
(c) He studied the relationship of sine to cosine.
(d) He studied the relationship between ratios in triangles.

5. What did Dunham claim about Archimedes's determination of a number value for pi?
(a) Archimedes's number was perfectly correct.
(b) Archimedes's number could have been better if he had understood Euclid's work better,
(c) Archimedes's number was not very accurate, considering the technology of his time.
(d) Archimedes's number was very good, considering he did not have a way to calculate square roots.

Short Answer Questions

1. Which of the following were an example of twin primes?

2. Which of the following was NOT one of the basic definitions in Elements?

3. Which of the following was NOT defined by Euclid?

4. What did Dunham consider extraordinary about the Elements?

5. What did Ferdinand Lindeman prove in 1882?

(see the answer key)

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