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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 to explain Archimedes determination of circular area.

Part 1) According to Archimedes what was pi, and why is this value needed to determine circular area?

Part 2) Explain how Archimedes used a right triangle to determine the area of a circle.

Part 3) Why was the determination of circular area useful at the time of Archimedes, and how did it advance the future of mathematics?

### Essay Topic 2

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?

### 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?

This section contains 906 words(approx. 4 pages at 300 words per page) |