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. Where was Archimedes born?

2. Which of the following is false about the modern implications of Euclid's number theory?

3. What do we know in modern times about Heron?

4. Which is one of the common notions presented in Elements?

5. In Elements, how many postulates must be accepted as given?

Short Essay Questions

1. Describe how Cardano eventually publishes the solution to cubic equations.

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

3. Describe what Gauss discovered according to Dunham.

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

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

6. Describe what the Egyptians knew about geometry and triangles before Hippocrates.

7. What was Euclid's definition of composite and perfect numbers?

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

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

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

In all of the great theorems presented in Dunham's book, which theorem do you think made the most impact on the history of mathematics? Write an essay to defend your opinion with reference to Dunham's descriptions and conclusions.

Essay Topic 2

Describe Gauss's work on what was to be known as non-euclidean geometry. What was Gauss's system for triangles where angles added up to fewer than 180 degrees? What were some of his conclusions? Did he publish his work? Was their any controversy surrounding his work on this system? Explain.

Essay Topic 3

Write an essay to describe what was known about mathematics and geometry before and in the time of Thales.

Part 1) Describe what we know about geometry before Thales.

Part 2) In what ways were mathematics and geometry used before Thales?

Part 3) Explain what we know about Thales' work. How did it advance mathematics?

(see the answer keys)

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