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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 did Hippocrates do that advanced mathematical methods?
(a) He created a new ways to disprove theories.
(b) He demonstrated that geometry does not have to be based on previous knowledge.
(c) He built theorems based on sequencially more complex proofs.
(d) He proved that mathematics can be applied in a unlogical order.

2. Which of the following could NOT be included as a step in Euclid's great theorem?
(a) Divide a infinite group of primes by the sum of their composites.
(b) Take a finite group of primes and add them together, plus one.
(c) If a new number is found to be composite, then it must have some prime as a divisor.
(d) After summation, the new number can be prime or composite.

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

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

5. "Straight lines in the same plane that will never meet if extended forever" is a definition of what?
(a) Intersection.
(b) Circle.
(c) 180 degree angle.
(d) Parallel lines.

Short Answer Questions

1. What instruments did the Greeks use to square a shape?

2. What did Ferdinand Lindeman prove in 1882?

3. What was Hippocrates's great advance to mathematics?

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

5. After Hippocrates, what shape did the Greeks attempt to square without success?

(see the answer key)

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