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Name: _________________________ | Period: ___________________ |

This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.

## Multiple Choice Questions

**1. Who was the first of ancient philosophers to consider why geometric properties existed?**
**(a)** Hippocrates. **(b)** Aristotle. **(c)** Thales. **(d)** Pythagoras.

**2. Which of Euclid's postulates troubled many of the following generations of mathematicians?**
**(a)** Euclid's postulate on right triangles. **(b)** Euclid's proof on right triangles. **(c)** Euclid's postulate on creating an arc. **(d)** Euclid's postulate on parallel lines.

**3. Exactly what limit is reached at a quartic equation?**
**(a)** The limit of the decompressed cubic method. **(b)** The limit of algebra. **(c)** The limit of logical geometric proofs. **(d)** The limit of the Pythagorean Theorem.

**4. Heron devised which of the following methods?**
**(a)** A way to determine the volume in a sphere. **(b)** A way to solve binomial equations. **(c)** A way to determine the area of a triangle. **(d)** A way to apply mathematics to public health.

**5. After working on pi, what did Archimedes continue with in his study of mathematics?**
**(a)** He studied the volume and surface area of spheres, cones, and cylinders. **(b)** He studied the volume to surface area ratios of cubes. **(c)** He studied the relationship of sine to cosine. **(d)** He studied the relationship between ratios in triangles.

## Short Answer Questions

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

**2.** Which is a geometric concept that humans have been aware of since the dawn of agriculture?

**3.** How did Archimedes arrive at a number value for pi?

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

**5.** Where was the modern number system developed?

## Short Essay Questions

**1.** What was Gauss's major unpublished achievement in geometry?

**2.** Explain who was Hippocrates, his contribution to mathematics, and how do we know about him?

**3.** How did Archimedes find a number value for pi?

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

**5.** What great theorems and work of Newton did Dunham highlight?

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

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

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

**9.** Describe what the Bernoullis discovered about series, and give an example.

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

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