*BookRags*. (c)2016 BookRags, Inc. All rights reserved.

Name: _________________________ | Period: ___________________ |

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

## Multiple Choice Questions

**1. What did Archimedes manage to prove using Euclid's ideas?**
**(a)** That the value of pi is proportional to the area of the circle. **(b)** That the area of a circle and the square of its diameter is really the same as the relationship of diameter to circumference. **(c)** That the relationship of area to circumference is really the same as the relationship of radius to diameter. **(d)** That the square of a diameter is equal to pi.

**2. Who was Heron?**
**(a)** A matematician from Alexanderia. **(b)** A politician from Rome. **(c)** A philosopher from Greece. **(d)** A physician from the far East.

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

**4. Which was true of Euclid's number theory?**
**(a)** It has been proven too basic to be useful. **(b)** It was incorrect, as proved by Plato. **(c)** It has an impact on modern math. **(d)** It was proven to the true by Hippocrates.

**5. How did Archimedes arrive at a number value for pi?**
**(a)** By proving that pi could not be a negative number. **(b)** By constructing successively smaller circles inside circles until he realized all of their ratios of diameter to area were equal. **(c)** By constructing multi-sided polygons inside and outside a circle and determining their perimeters. **(d)** By proving pi could not be equal to one.

## Short Answer Questions

**1.** How did Archimedes demonstrate his theory of pi?

**2.** Which of the following was NOT defined by Euclid?

**3.** Heron's work referred to the work of what other famous scholar?

**4.** Which of the following is an example of a perfect number?

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

## Short Essay Questions

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

**2.** What was already known about circles before Archimedes?

**3.** Describe Lindeman's work on the square of a circle, and state what he discovered.

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

**5.** Summarize, in a sentence, what was Hippocates's great theorem, and what was it based on according to Dunham?

**6.** Explain in two sentences Euclid's method to prove the Pythagorean Theorem.

**7.** What did Dunham claim was Pythagoras's major contribution to geometry, and mathematical reasoning?

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

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

**10.** Explain who was Gerolamo Cardano, and how did he become involved with the solution to the cubic.

This section contains 1,018 words(approx. 4 pages at 300 words per page) |