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 did Euclid state about pi in Elements?
(a) There is no relationship between the area of a circle and its circumference.
(b) The proportion of diameter to area is never equal.
(c) The proportion of area to circumference is never equal.
(d) There is a constant relationship between the area of a circle and the square of its diameter.

2. What name did Euclid give for numbers that could be divided by numbers other than themselves and one?
(a) Even numbers.
(b) Discrete numbers.
(c) Perfect numbers.
(d) Composite numbers.

3. Which city was the center of thinking and learning in Third century BC?
(a) Alexandria.
(b) Olympia.
(c) Athens.
(d) Rome.

4. Where did Hippocrates come from?
(a) Chios.
(b) Athens.
(c) Rome.
(d) Constinople.

5. What allowed Cardano to justify publishing his book?
(a) He was dead, and the book was really published by his student.
(b) He was punished as a heretic,
(c) He found Fior's documents which spoke against Tartaglia.
(d) He found del Ferro's orgininal solution to the cubic.

Short Answer Questions

1. Where was Archimedes born?

2. After working on pi, what did Archimedes continue with in his study of mathematics?

3. Why did Cardano take an oath to secrecy?

4. Which of the following is true in modern math about twin primes?

5. What was true about Heron's theorem as described by Dunham?

Short Essay Questions

1. What did Dunham claim was Pythagoras's major contribution to geometry, and mathematical reasoning?

2. Describe what Gauss discovered according to Dunham.

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

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

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

6. Explain in two sentences Euclid's method to prove the Pythagorean Theorem.

7. Describe what work of Euclid's fascinated Plato and his theory on the shape of the Universe.

8. What did Dunham describe in the epilogue of the chapter?

9. Explain when the knowledge of ancient scholars was rediscovered.

10. Describe Lindeman's work on the square of a circle, and state what he discovered.

(see the answer keys)

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