Journey Through Genius: The Great Theorems of Mathematics Quiz | Eight Week Quiz E

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

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

3. What did Dunham describe about the following series 1 + 2 + 3 + 4. . .?
(a) The sum diverges to infinity.
(b) The sum converges to infinity.
(c) The sum grows ever smaller.
(d) The sum converges to a finite term.

4. Dunham showed that Heron's proof could also be used as which of the following?
(a) A proof of Archimedes' number theory.
(b) A proof of the Pythagorean Theorem.
(c) A proof of Euclid's number theory
(d) A proof of Hippocrates' squared areas.

5. What was Euclid's definition of a prime number?
(a) Numbers which do not, and can not, contain a perfect number.
(b) Numbers which can only be divided by themselves and 1.
(c) Numbers which contain an infinite number of composite numbers.
(d) Numbers which are divisible by 2.

Short Answer Questions

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

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

3. Which mathematician was first to take the challenge to solve cubic equations?

4. What was the same about the series proposed by Leibniz and the series proposed by Bernoulli?

5. Which of the following is an example of a perfect number?

(see the answer key)

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