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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 is one of the common notions presented in Elements?**
**(a)** "Things which are equal to the same thing are also equal to each other." **(b)** "Points with equal values can be connected with a line of equal value." **(c)** "The inverse of a line makes a circle." **(d)** "Things with are equal have an inverse that is equal."

**2. Which of the following is false about the modern implications of Euclid's number theory?**
**(a)** Great mathematicians continue to puzzle over some aspects of Euclid's number theory. **(b)** Whether there are no odd perfect numbers is still not known. **(c)** Euclid's recipe for constructing even perfect numbers is incorrect. **(d)** Euclid gave a good idea for how to construct even perfect numbers.

**3. Which words best describe how solid proofs were developed in Elements?**
**(a)** Inverted scaffold. **(b)** Simple arguments. **(c)** Programmed order. **(d)** Axiomatic framework.

**4. How did Lindeman prove his conclusion?**
**(a)** Lindeman proved that some numbers are constructable without the use of a compass. **(b)** Lindeman proved that all numbers are constructable with a compass and ruler. **(c)** Lindeman proved that some numbers are not constructable with only a compass and straight-edge. **(d)** Lindeman proved that square roots are irrational numbers.

**5. What did the Pythagorean Theorem accomplish for mathematics?**
**(a)** The ability to find square roots. **(b)** The concept of providing a logical proof. **(c)** The concept of constructing useful mathematics. **(d)** The ability to measure angles.

## Short Answer Questions

**1.** Which of the following is an example of a postulate that must be accepted in Elements?

**2.** Numbers whose divisor add up to itself, was considered which type of number according to Euclid?

**3.** Which of the following was NOT one of Gauss' discoveries?

**4.** Which of the following could NOT be included as a step in Euclid's great theorem?

**5.** Which of the following was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?

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