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

## Multiple Choice Questions

**1. What was the bases of Hippocrates's proof ?**
**(a)** Properties of points and lines. **(b)** Properties of triangles and semicircles. **(c)** Properties of squares and cubes. **(d)** Properties of area to volume measurements.

**2. Which of the following best describes Cardano's character?**
**(a)** Religious. **(b)** Eccentric. **(c)** Arrogant. **(d)** Flirtacious.

**3. 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 relationship of sine to cosine. **(c)** He studied the relationship between ratios in triangles. **(d)** He studied the volume to surface area ratios of cubes.

**4. What instruments did the Greeks use to square a shape?**
**(a)** A compass and a ruled straight-edge. **(b)** A small grid. **(c)** A pendulum. **(d)** A sphere and ruler.

**5. Which is one of the common notions presented in Elements?**
**(a)** "Things which are equal to the same thing are also equal to each other." **(b)** "Things with are equal have an inverse that is equal." **(c)** "Points with equal values can be connected with a line of equal value." **(d)** "The inverse of a line makes a circle."

## Short Answer Questions

**1.** Dunham showed that Heron's proof could also be used as which of the following?

**2.** What was the title of Cardano's book which contained the solution to the cubic?

**3.** What name did Euclid give for numbers that could be divided by numbers other than themselves and one?

**4.** Where was Archimedes born?

**5.** In what time period did mathematicians find a solution to cubic equations?

## 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.

This section contains 843 words(approx. 3 pages at 300 words per page) |