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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. As described by Archimedes, what is always true about he diameter of the circle?
(a) It's equal to pi.
(b) It's never proportional to its circumference.
(c) It's equal to the square of the radius.
(d) It's always proportional to its circumference.

2. To how many decimal places did Newton determine the number for pi?
(a) Eight places.
(b) Three places.
(c) Nine places.
(d) Twelve places.

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

4. What is true about the successive squared denominator series proposed by the Bernoullis?
(a) The sum converges.
(b) The sum diverges into infinity.
(c) The sum converges to 2.
(d) The sum diverges.

5. What series was Euler most famous for?
(a) 1 + 1/2³ + 1/3³ + 1/4³ . . . 1/k³ . . .
(b) 1 + 1/2 + 1/6 + 1/10 + 1/15 . . .
(c) 1 + 1/4 + 1/9 + 1/16 . . . + 1/k² . . .
(d) 1 + 1/2 + 3/4 + 4/5 . . .

Short Answer Questions

1. Which of the following was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?

2. What did Dunham consider as Archimedes's "masterpiece"?

3. When was Euler born?

4. In Elements, how many postulates must be accepted as given?

5. Which of the following is true about pi, as described by Dunham.

(see the answer key)

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