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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 of the following was an important proposition given by Euclid's number theory?
(a) Numbers from one to ten are only divisible by composite numbers.
(b) Any even number is divisible by 3.
(c) Any perfect number is divisible by some composite number.
(d) Any composite number is divisible by some prime number.

2. 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 a side whose square is the sum of the squares of the two legs.
(d) When a triangle has three sides whose squares are equal to the area of the triangle.

3. In Elements, how many postulates must be accepted as given?
(a) Eighteen.
(b) Twelve,
(c) Five.
(d) Twenty-two.

4. What was most useful about finding the square of a shape, before Hippocrates?
(a) It was useful in creating simple elevation maps,
(b) It was useful in finding the area of oddly shaped pieces of land.
(c) It was useful in finding the area of circles.
(d) It was useful in determining the distance between two points.

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

Short Answer Questions

1. What did Ferdinand Lindeman prove in 1882?

2. How did Lindeman prove his conclusion?

3. Where did Hippocrates come from?

4. Who was the author of the book Elements?

5. How many definitions were stated in Elements?

(see the answer key)

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