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

Name: _________________________ | Period: ___________________ |

This quiz consists of 5 multiple choice and 5 short answer questions through Archimedes' Determination of Circular Area.

## Multiple Choice Questions

**1. As described by Archimedes, what is always true about he diameter of the circle?**
**(a)** It's never proportional to its circumference. **(b)** It's equal to the square of the radius. **(c)** It's always proportional to its circumference. **(d)** It's equal to pi.

**2. According to Euclid, when is a triangle a right triangle?**
**(a)** When a triangle has three sides whose squares are equal to the area of the triangle. **(b)** When a triangle does not have a side which can be considered a hypotenuse. **(c)** When a triangle has a side whose square is the sum of the squares of the two legs. **(d)** When a triangle can be constructed with three unequal sides.

**3. What range of values did Archimedes determine for pi?**
**(a)** Between 3 and 3 1/2. **(b)** Between 3 and 4. **(c)** Between 3 1/2 and 3 5/8. **(d)** Between 3 10/11 and 3 1/7.

**4. What was Hippocrates famous for?**
**(a)** His ability to construct circles without a compass. **(b)** His theorem on the quadrature of the lune. **(c)** His proof on right triangles. **(d)** His proof defining gravity.

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

## Short Answer Questions

**1.** Which of the following is true in modern math about twin primes?

**2.** What did Hippocrates do that advanced mathematical methods?

**3.** Where did Hippocrates come from?

**4.** In what century did Archimedes live?

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

This section contains 439 words(approx. 2 pages at 300 words per page) |