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

2. According to Dunham, who was most able to collect knowledge from around the globe?
(a) Arabian scholars.
(b) Greek philosophers.
(c) Greek tradesman.
(d) Roman emporers.

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

4. Which is one of the common notions presented in Elements?
(a) "Things which are equal to the same thing are also equal to each other."
(b) "The inverse of a line makes a circle."
(c) "Things with are equal have an inverse that is equal."
(d) "Points with equal values can be connected with a line of equal value."

5. Which of the following can not be solved using algebra?
(a) Quintic equation.
(b) Triangulation.
(c) Geometric equation.
(d) Quadratic equation.

Short Answer Questions

1. Who challenged Tartaglia to a contest to solve cubic equations?

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

3. What did Dunham discuss for many pages in this chapter?

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

5. What was Eratosthanes most famous for?

Short Essay Questions

1. Describe who was Archimedes and how Dunham described his character.

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

3. Why did Euclid's postulate on parallel lines trouble mathematicians for centuries?

4. Explain what Archimedes went on to study after the circle, and what was Dunham's opinion of this work.

5. Summarize, in a sentence, what was Hippocates's great theorem, and what was it based on according to Dunham?

6. How did Heron find the area of a triangle, and what did Dunham state about Heron's work?

7. Describe what is quadrature and why it was useful in the time of Hippocrates.

8. Explain who was Gerolamo Cardano, and how did he become involved with the solution to the cubic.

9. Explain some puzzles suggested by Euclid's theories.

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

(see the answer keys)

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