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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. How did Archimedes demonstrate his theory of pi?**
**(a)** He demonstrated that the area of the circle is never equal to the area of the triangle. **(b)** He demonstrated that the area of the circle is always greater than the area of the triangle. **(c)** He demonstrated that the area of the circle is never less than the area of the triangle. **(d)** He demonstrated that the area of the circle is neither greater than nor less than the area of the triangle and therefore must be equal to it.

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

**3. What was Euclid's definition of a prime number?**
**(a)** Numbers which do not, and can not, contain a perfect number. **(b)** Numbers which can only be divided by themselves and 1. **(c)** Numbers which are divisible by 2. **(d)** Numbers which contain an infinite number of composite numbers.

**4. What was Hippocrates's great advance to mathematics?**
**(a)** He showed how to square a figure with curved sides. **(b)** He showed how to find the angles in a right triangle. **(c)** He showed how to square a circle. **(d)** He showed how to simplify the area of a triangle.

**5. As described by Dunham, what did Archimedes demonstrate first in his proof on pi?**
**(a)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's diameter. **(b)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's circumference. **(c)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's diameter and the other leg equal to the circle's circumference. **(d)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's hypotenuse and the other leg equal to the circle's circumference.

## Short Answer Questions

**1.** What was most useful about finding the square of a shape, before Hippocrates?

**2.** Which of the following was one of Euclid's great theorems?

**3.** "Straight lines in the same plane that will never meet if extended forever" is a definition of what?

**4.** In general, what did Euclid's number theory describe?

**5.** How did Archimedes arrive at a number value for pi?

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