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## Mid-Book Test - Hard

Name: _________________________ | Period: ___________________ |

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

## Short Answer Questions

**1. What was the bases of Hippocrates's proof ?**

**2. Which of the following best describes Cardano's character?**

**3. After working on pi, what did Archimedes continue with in his study of mathematics?**

**4. What instruments did the Greeks use to square a shape?**

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

## Short Essay Questions

**1. Describe what mathematical and artistic movements are focused on in the second half of the 19th century.**

**2. Describe the connection between Fermat and Euler's work.**

**3. Where did the center of mathematical thinking shift to in the !7th Century, and who are the major scholars of this time period?**

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

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

**6. Describe the great theorem explained by Dunham in this chapter.**

**7. Describe who was Archimedes and how Dunham described his character.**

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

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

**10. Describe what Gauss discovered according to Dunham.**

## Essay Topics

### Essay Topic 1

Write a three part essay on the lives and work of both Euler and Gauss.

Part 1) What was similar about Euler and Gauss from an early age? What characteristics did they have in common?

Part 2) Give some examples of great theorems proposed by Euler and by Gauss. Do you think their work had anything in common mathematically?

Part 3) What could be considered Euler's greatest work? What could be considered Gauss's greatest work? How did both mathematicians advance the study of mathematics?

### 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

Explain the accuracy of Archimedes determination of pi. How did he determine the number value of pi? How accurate is Archimedes's measurement of pi? What other mathematician was able to determine a number value, though more accurate, for pi?

This section contains 919 words(approx. 4 pages at 300 words per page) |