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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 one of Euclid's great theorems?
(a) There exists only infinite and whole numbers.
(b) There exists an finite number of prime numbers.
(c) Prime numbers are more comples than discrete numbers.
(d) There exists an infinite number of prime numbers.

2. What did Euclid state about pi in Elements?
(a) There is no relationship between the area of a circle and its circumference.
(b) The proportion of area to circumference is never equal.
(c) The proportion of diameter to area is never equal.
(d) There is a constant relationship between the area of a circle and the square of its diameter.

3. How did Euler prove if the number 4,294,967,297 was prime or composite?
(a) He divided it by 2.
(b) He factored it.
(c) He used his own rule of squares.
(d) He used Newton's calulus methods.

4. What did Archimedes manage to prove using Euclid's ideas?
(a) That the relationship of area to circumference is really the same as the relationship of radius to diameter.
(b) That the value of pi is proportional to the area of the circle.
(c) That the square of a diameter is equal to pi.
(d) That the area of a circle and the square of its diameter is really the same as the relationship of diameter to circumference.

5. What is a "depressed cubic"?
(a) A method to simpify the x squared value in a cubic equation.
(b) A method to simplify measuring complex geometric forms.
(c) A method to logically square all the factors in a cubic equation.
(d) A method to solve equations with two variables.

Short Answer Questions

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

2. Where was Archimedes born?

3. Which of the following was NOT one of Gauss' discoveries?

4. Who was Neil's Abel?

5. What did Plato use his inspiration from Euclid for?

(see the answer key)

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