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 did the Pythagorean Theorem accomplish for mathematics?

2. Which was true of Euclid's number theory?

3. Exactly what limit is reached at a quartic equation?

4. Where was Neil's Abel from?

5. Which of the following is true about pi, as described by Dunham.

Short Essay Questions

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

2. Describe the contents of Cardano's book.

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

4. What was already known about circles before Archimedes?

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

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

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. According the Dunham, how did Euclid prove his theory on the infinitude of primes?

10. Describe the events that follow del Ferro's death between Fior and Tartaglia.

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Compare Pythagoras's proof of the Pythagorean Theorem and how Heron's formula for triangular area can be used as an alternative proof of the Pythagorean theorem. What are the common assumptions in both proofs? What components of each proof are different?

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 a three part essay to describe third century Alexandra.

Part 1) Describe the geographic location of Alexandria. Why did its location affect its scholars?

Part 2) Name and describe the work of a few scholars in third century Alexandria.

Part 3) Who was Heron? How did his achievements improve mathematics?

(see the answer keys)

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