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This quiz consists of 5 multiple choice and 5 short answer questions through A Sampler of Euler's Number Theory.

Multiple Choice Questions

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

2. Who acted as the gate keepers of knowledge?
(a) Greek philosophers.
(b) Arabian scholars.
(c) Roman emporers.
(d) Greek tradesman.

3. Which of the following is INCORRECT, and not used in Archimedes proof of his theory?
(a) Since the diameter of a circle is equal to the hypotenuse of the right triangle, the area of the triangle in his proof is 1/2 the radius times the circumference.
(b) Since the circumference can also be expressed as twice the radius multiplied by π, the area is 2πr²/2, or πr².
(c) Since the base of the triangle is equal to the circumference and the height is the radius, the area of the triangle in his proof is 1/2 the radius times the circumference.
(d) The area of a triangle is one half the base times the height.

4. What was most noticeable about Euler at a young age?
(a) He had an aptitude for literature.
(b) He was very athletic.
(c) He was not very quick with arithmatic.
(d) He had a remarkable memory.

5. What was known about pi, during Archimedes' time?
(a) That is was the relationship between the diameter and circumference of a circle.
(b) That it could not be assigned a relationship between measurements in a circle.
(c) Nothing, the concept of pi was unknown.
(d) That it was never the same number value for a given circle.

Short Answer Questions

1. How did Archimedes arrive at a number value for pi?

2. Which of the following was one of Euclid's great theorems?

3. Which of the following becomes an important definition in mathematics that was first presented in Elements?

4. Which of the following is an example of a postulate that must be accepted in Elements?

5. What name did Euclid give for numbers that could be divided by numbers other than themselves and one?

(see the answer key)

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