Journey Through Genius: The Great Theorems of Mathematics Test | Mid-Book Test - Medium

William Dunham (mathematician)
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This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.

Multiple Choice Questions

1. Who was the first of ancient philosophers to consider why geometric properties existed?
(a) Hippocrates.
(b) Aristotle.
(c) Thales.
(d) Pythagoras.

2. Which of Euclid's postulates troubled many of the following generations of mathematicians?
(a) Euclid's postulate on right triangles.
(b) Euclid's proof on right triangles.
(c) Euclid's postulate on creating an arc.
(d) Euclid's postulate on parallel lines.

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

4. Heron devised which of the following methods?
(a) A way to determine the volume in a sphere.
(b) A way to solve binomial equations.
(c) A way to determine the area of a triangle.
(d) A way to apply mathematics to public health.

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

Short Answer Questions

1. Which of the following is false about the modern implications of Euclid's number theory?

2. Which is a geometric concept that humans have been aware of since the dawn of agriculture?

3. How did Archimedes arrive at a number value for pi?

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

5. Where was the modern number system developed?

Short Essay Questions

1. What was Gauss's major unpublished achievement in geometry?

2. Explain who was Hippocrates, his contribution to mathematics, and how do we know about him?

3. How did Archimedes find a number value for pi?

4. Describe the great theorem explained by Dunham in this chapter.

5. What great theorems and work of Newton did Dunham highlight?

6. Describe the ancient city Alexandria and name a few of its third century geniuses.

7. What did Dunham explain about the shift in learning from the West to the East?

8. Explain why Archimedes finding a number value for pi was considered a great achievement according to Dunham.

9. Describe what the Bernoullis discovered about series, and give an example.

10. Describe the connection between Fermat and Euler's work.

(see the answer keys)

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