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 could NOT be included as a step in Euclid's great theorem?
(a) After summation, the new number can be prime or composite.
(b) Take a finite group of primes and add them together, plus one.
(c) Divide a infinite group of primes by the sum of their composites.
(d) If a new number is found to be composite, then it must have some prime as a divisor.

2. "Straight lines in the same plane that will never meet if extended forever" is a definition of what?
(a) Circle.
(b) Parallel lines.
(c) 180 degree angle.
(d) Intersection.

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

4. How many definitions were stated in Elements?
(a) Five.
(b) Twenty-three.
(c) Thirty.
(d) Eighteen.

5. Where was Archimedes born?
(a) Rome.
(b) Sicily.
(c) Olympia.
(d) Athens.

Short Answer Questions

1. What was Hippocrates's great advance to mathematics?

2. What was the bases of Hippocrates's proof ?

3. Which of the following is true about pi, as described by Dunham.

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

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

(see the answer key)

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