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 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 del Ferro's orgininal solution to the cubic.
(d) He found Fior's documents which spoke against Tartaglia.

2. In Elements, how many postulates must be accepted as given?
(a) Twenty-two.
(b) Eighteen.
(c) Five.
(d) Twelve,

3. Who acted as the gate keepers of knowledge?
(a) Greek tradesman.
(b) Roman emporers.
(c) Greek philosophers.
(d) Arabian scholars.

4. What provided most of the content in the book Elements?
(a) Hypotheses.
(b) Notions.
(c) Postulates.
(d) Propositions.

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

Short Answer Questions

1. Which of the following was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?

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

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

4. What shape was NOT demonstrated in the Elements as having a relationship to other shapes?

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

Short Essay Questions

1. Describe why Dunham infers that Euclid's Elements was an evolutionary book not so much for what it said, but in how it was presented.

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

3. Explain what Neils Abel proved.

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

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

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

7. Describe Euclid's postulates and notions in how they were important in constructing his proofs.

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

9. Who was Luca Pacioli, and what controversy was sparked over his writings?

10. How many definitions were in Euclid's book? List some of the definitions he included.

(see the answer keys)

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