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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. Who was the first of ancient philosophers to consider why geometric properties existed?
(a) Aristotle.
(b) Pythagoras.
(c) Hippocrates.
(d) Thales.

2. What did Euclid do in his 48th proposition?
(a) Euclid demonstrated how to use the Pythagorean Theorem.
(b) Euclid demonstrated the faults of the Pythagorean Theorem.
(c) Euclid proved the converse of the Pythagorean Theorem.
(d) Euclid proved the Pythagorean Theorem.

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

4. Which of the following were an example of twin primes?
(a) 11 and 13.
(b) 19 and 22.
(c) 2 and 6.
(d) 15 and 16.

5. What did Gauss set out to prove?
(a) That a right angle is always equal to 90 degrees.
(b) That the sum of the angles in a triangle is 180 degrees.
(c) That Euclid's postulate on straight lines was incorrect.
(d) That a circle can have less than 360 degrees.

Short Answer Questions

1. How do we know about Hippocrates proofs and theorems?

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

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

4. What is the name for determining the area of an enclosed space by constructing a square of equivalent area?

5. How many definitions were stated in Elements?

(see the answer key)

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