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

William Dunham (mathematician)
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This test consists of 5 short answer questions, 10 short essay questions, and 1 (of 3) essay topics.

Short Answer Questions

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

2. Which of the following can not be solved using algebra?

3. Who was the author of the book Elements?

4. What did Euclid do in his 48th proposition?

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

Short Essay Questions

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

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

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

4. 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.

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

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

7. What was already known about circles before Archimedes?

8. Describe in two sentences Archimedes's method for determining circular area.

9. Who was Heron, and what is known about him today?

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Dunham presented a number of controversies over publication and intellectual property rights in the history of mathematics. Explain what seems to be the common issues historically in the publication of one's discoveries. Describe what conditions often lead to controversy over intellectual property rights.

Essay Topic 2

Write a three part essay to compare the work of Euclid to the work of Gauss.

Part 1) Explain what concepts both Euclid and Gauss worked with, and how they approached a similar problem.

Part 2) Compare what Euclid believed about triangles to what Gauss believed about triangles.

Part 3) How did both Gauss and Euclid advance mathematical understanding in their own time?

Essay Topic 3

Write an essay to explain what is meant by "infinitude of primes." Use the following questions to guide your writing. What was Euclid's definition of a prime number? How were prime and composite numbers related according to Euclid?

(see the answer keys)

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