View a FREE sample

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

Short Answer Questions

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

2. What did Dunham consider extraordinary about the Elements?

3. What does the Pythagorean Theorem state?

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

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

Short Essay Questions

1. Describe what Gauss discovered according to Dunham.

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

3. What did Dunham explain about the shift in learning from the West to the East?

4. Summarize, in a sentence, what was Hippocates's great theorem, and what was it based on according to Dunham?

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

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

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

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

9. Describe the contents of Cardano's book.

10. Describe Euclid's definition of prime numbers and the relationship he stated as existing between prime and composite numbers.

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

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 2

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.

Essay Topic 3

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?

(see the answer keys)

This section contains 864 words (approx. 3 pages at 300 words per page) View a FREE sample