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. Which words best describe how solid proofs were developed in Elements?

2. Which of the following is INCORRECT, and not used in Archimedes proof of his theory?

3. What did Heron's advances put into historical perspective for Dunham?

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

5. Besides being a mathematician, what else other work was Archimedes famous for?

Short Essay Questions

1. Explain why Archimedes finding a number value for pi was considered a great achievement according to Dunham.

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

3. How did Heron find the area of a triangle, and what did Dunham state about Heron's work?

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

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

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

7. Describe what Gauss discovered according to Dunham.

8. Explain what Neils Abel proved.

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

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

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

Describe how Gerolamo Cardano became involved in the solution to cubic equations. Why was their a controversy over his publication of the solution to cubic equations? Explain.

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