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

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

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

**4. Which of the following is true in modern math about twin primes?**
**(a)** They are not considered whole numbers. **(b)** They are infinite. **(c)** We don't know if they are finite or infinite. **(d)** Their sum is always another prime number.

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

## Short Answer Questions

**1.** After Hippocrates, what shape did the Greeks attempt to square without success?

**2.** What provided most of the content in the book Elements?

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

**4.** Who was the first of ancient philosophers to consider why geometric properties existed?

**5.** Which is one of the common notions presented in Elements?

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