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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 becomes an important definition in mathematics that was first presented in Elements?
(a) Intersection.
(b) 180 degree angle.
(c) Circle.
(d) Parallel line.

2. Which of Euclid's postulates troubled many of the following generations of mathematicians?
(a) Euclid's postulate on right triangles.
(b) Euclid's postulate on creating an arc.
(c) Euclid's postulate on parallel lines.
(d) Euclid's proof on right triangles.

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

4. Which of the following was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?
(a) Euclid used his own axioms and propositions to show relationships,
(b) Euclid stated that the diagonal hypotenuse of a right triangle is equal to the sums of the squares of the two legs.
(c) Euclid used propositions about similar angles and parallel lines.
(d) Euclid constructed squares on the sides of right triangles.

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

Short Answer Questions

1. According to Euclid, when is a triangle a right triangle?

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

3. Which words best describe how solid proofs were developed in Elements?

4. Which of the following was NOT one of the basic definitions in Elements?

5. What was Euclid's definition of a prime number?

(see the answer key)

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