## Mid-Book Test - Medium

Name: _________________________ | Period: ___________________ |

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) |