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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 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 diameter and the other leg equal to the circle's circumference. **(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 diameter. **(c)** 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. **(d)** 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.

**2. Which of the following was one of Euclid's great theorems?**
**(a)** There exists an finite number of prime numbers. **(b)** There exists an infinite number of prime numbers. **(c)** There exists only infinite and whole numbers. **(d)** Prime numbers are more comples than discrete numbers.

**3. What is the name for determining the area of an enclosed space by constructing a square of equivalent area?**
**(a)** Quadrature. **(b)** Triangulation. **(c)** Square root. **(d)** Cubation.

**4. What does the Pythagorean Theorem state?**
**(a)** For any triangle the sum of the legs squared is equal to the length of the hypotenuse. **(b)** For any triangle the sqaured sum of the legs is equal to half the hypotenuse. **(c)** For any right triangle the square of the diagonal side is equal to the sum of the squares of the two legs. **(d)** For any right triangle the diagonal side is equal to the sum of the legs.

**5. How many sides did the pentadecagon have, as presented by Euclid?**
**(a)** Five. **(b)** Ten. **(c)** Twenty. **(d)** Fifteen.

## Short Answer Questions

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

**2.** How did Lindeman prove his conclusion?

**3.** That properties of specific shapes were early Egyptians aware of?

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

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

This section contains 472 words(approx. 2 pages at 300 words per page) |