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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 name did Euclid give for numbers that could be divided by numbers other than themselves and one?
(a) Discrete numbers.
(b) Composite numbers.
(c) Even numbers.
(d) Perfect numbers.

2. What was the bases of Hippocrates's proof ?
(a) Properties of points and lines.
(b) Properties of area to volume measurements.
(c) Properties of triangles and semicircles.
(d) Properties of squares and cubes.

3. What does the Pythagorean Theorem state?
(a) For any right triangle the diagonal side is equal to the sum of the legs.
(b) For any triangle the sum of the legs squared is equal to the length of the hypotenuse.
(c) For any triangle the sqaured sum of the legs is equal to half the hypotenuse.
(d) For any right triangle the square of the diagonal side is equal to the sum of the squares of the two legs.

4. How did Lindeman prove his conclusion?
(a) Lindeman proved that all numbers are constructable with a compass and ruler.
(b) Lindeman proved that some numbers are constructable without the use of a compass.
(c) Lindeman proved that square roots are irrational numbers.
(d) Lindeman proved that some numbers are not constructable with only a compass and straight-edge.

5. Which of the following was NOT defined by Euclid?
(a) Even numbers.
(b) Odd numbers.
(c) Nominal numbers.
(d) Whole numbers.

Short Answer Questions

1. In general, what did Euclid's number theory describe?

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

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

4. What did Dunham consider extraordinary about the Elements?

5. Numbers whose divisor add up to itself, was considered which type of number according to Euclid?

(see the answer key)

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