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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 always proportional to its circumference. **(c)** It's equal to the square of the radius. **(d)** It's equal to pi.

**2. Which of the following was NOT one of Gauss' discoveries?**
**(a)** That there is no apparent contraction to the assumption that the sum of angles in a triangle can have fewer than 180 degrees. **(b)** That under Euclid's definition parallel lines can intersect. **(c)** That angles in a triangles can not add up to more than 180 degrees. **(d)** "Non-euclidean" geometry.

**3. 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 can be constructed with three unequal sides. **(c)** When a triangle has a side whose square is the sum of the squares of the two legs. **(d)** When a triangle does not have a side which can be considered a hypotenuse.

**4. Where did Hippocrates come from?**
**(a)** Athens. **(b)** Rome. **(c)** Chios. **(d)** Constinople.

**5. Which of the following is an example of a postulate that must be accepted in Elements?**
**(a)** It is possible to draw an arc with any three points. **(b)** It is possible to draw a straight line between an infinite number of points. **(c)** It is possible to draw a circle that contains no lines. **(d)** It is possible to connect any two points with a line and make a circle.

## Short Answer Questions

**1.** Which was true of Euclid's number theory?

**2.** Which of Euclid's postulates troubled many of the following generations of mathematicians?

**3.** Which of the following becomes an important definition in mathematics that was first presented in Elements?

**4.** Which of the following was NOT true about Archimedes, according to Dunham?

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

This section contains 392 words(approx. 2 pages at 300 words per page) |