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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. What name did Euclid give for numbers that could be divided by numbers other than themselves and one?
(a) Composite numbers.
(b) Even numbers.
(c) Perfect numbers.
(d) Discrete numbers.

2. Which of the following is an example of a perfect number?
(a) 6.
(b) 10.
(c) 1.
(d) 20.

3. What did Plato use his inspiration from Euclid for?
(a) To classify geometric shapes by their complexity.
(b) To prove Euclid's number theory was incorrect.
(c) To construct his theory on the shape of the Universe.
(d) To create a new theorem of algebra.

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

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

Short Answer Questions

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

2. What were the proofs in Elements based on?

3. What was true about Hippocrates's proof?

4. In general, what did Euclid's number theory describe?

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

(see the answer key)

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