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This quiz consists of 5 multiple choice and 5 short answer questions through The Bernoullis and the Harmonic Series.

Multiple Choice Questions

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

2. Exactly what limit is reached at a quartic equation?
(a) The limit of algebra.
(b) The limit of logical geometric proofs.
(c) The limit of the decompressed cubic method.
(d) The limit of the Pythagorean Theorem.

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

4. Which of the following is a series that the Bernoullis proposed did not converge on a finite sum?
(a) 1 + 1/2 + 3/4 + 4/5 . . .
(b) 1 + 1/2 + 1/6 + 1/10 + 1/15 . . .
(c) 1 + 1/2 + 1/3 + 1/4 + 1/5 . . . 1/1000 . . .
(d) 1 + 2 + 3 + 4 + 5. . .

5. What was true about Heron's theorem as described by Dunham?
(a) It was to determine the volume of a sphere without measuring the circumference.
(b) It was to find the area of a triangle when only the length of the sides are known.
(c) It was to solve equations were only two varibles are known.
(d) It was to determine the area of a circle by measuring a right triangle inside the circle.

Short Answer Questions

1. Who were Johann and Jakob Bernoulli?

2. In what century did Archimedes live?

3. How did Lindeman prove his conclusion?

4. What provided most of the content in the book Elements?

5. What did Newton's calculus involve?

(see the answer key)

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