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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. Numbers whose divisor add up to itself, was considered which type of number according to Euclid?
(a) Nominal number.
(b) Even number.
(c) Composite number.
(d) Perfect number.

2. What did Ferdinand Lindeman prove in 1882?
(a) That the square root of the hypotenuse of a right triangle can not be found.
(b) That the square of a circle can not be found with a compass and a straight-edge.
(c) It is possible to find the square of a circle.
(d) It is impossible to find the square of a semicircle.

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

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 some numbers are not constructable with only a compass and straight-edge.
(c) Lindeman proved that all numbers are constructable with a compass and ruler.
(d) Lindeman proved that square roots are irrational numbers.

5. Which of the following is an example of a postulate that must be accepted in Elements?
(a) It is possible to connect any two points with a line and make a circle.
(b) It is possible to draw a circle that contains no lines.
(c) It is possible to draw a straight line between an infinite number of points.
(d) It is possible to draw an arc with any three points.

Short Answer Questions

1. What was true about Hippocrates's proof?

2. Which of the following is true in modern math about twin primes?

3. "Straight lines in the same plane that will never meet if extended forever" is a definition of what?

4. What was Hippocrates famous for?

5. That properties of specific shapes were early Egyptians aware of?

(see the answer key)

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