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This quiz consists of 5 multiple choice and 5 short answer questions through Euclid and the Infinitude of Primes.

## Multiple Choice Questions

**1. Which was true of Euclid's number theory?**
**(a)** It has been proven too basic to be useful. **(b)** It was proven to the true by Hippocrates. **(c)** It was incorrect, as proved by Plato. **(d)** It has an impact on modern math.

**2. How do we know about Hippocrates proofs and theorems?**
**(a)** What we know is from references of later mathematicians. **(b)** Mathematicians rewrote all of his proofs after his death, **(c)** What is known from archived documents of his time. **(d)** His books and publications.

**3. How many definitions were stated in Elements?**
**(a)** Eighteen. **(b)** Five. **(c)** Thirty. **(d)** Twenty-three.

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

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

## Short Answer Questions

**1.** What was Euclid's definition of a prime number?

**2.** Which shapes as described by Euclid, inspired the Greek philosopher Plato?

**3.** Which words best describe how solid proofs were developed in Elements?

**4.** Who was the author of the book Elements?

**5.** What did the Pythagorean Theorem accomplish for mathematics?

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