Journey Through Genius: The Great Theorems of Mathematics Test | Mid-Book Test - Medium

William Dunham (mathematician)
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This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.

Multiple Choice Questions

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

2. Who was Heron?
(a) A matematician from Alexanderia.
(b) A politician from Rome.
(c) A philosopher from Greece.
(d) A physician from the far East.

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

4. Which was true of Euclid's number theory?
(a) It has been proven too basic to be useful.
(b) It was incorrect, as proved by Plato.
(c) It has an impact on modern math.
(d) It was proven to the true by Hippocrates.

5. How did Archimedes arrive at a number value for pi?
(a) By proving that pi could not be a negative number.
(b) By constructing successively smaller circles inside circles until he realized all of their ratios of diameter to area were equal.
(c) By constructing multi-sided polygons inside and outside a circle and determining their perimeters.
(d) By proving pi could not be equal to one.

Short Answer Questions

1. How did Archimedes demonstrate his theory of pi?

2. Which of the following was NOT defined by Euclid?

3. Heron's work referred to the work of what other famous scholar?

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

5. Dunham showed that Heron's proof could also be used as which of the following?

Short Essay Questions

1. Explain why Archimedes finding a number value for pi was considered a great achievement according to Dunham.

2. What was already known about circles before Archimedes?

3. Describe Lindeman's work on the square of a circle, and state what he discovered.

4. How did Archimedes find a number value for pi?

5. Summarize, in a sentence, what was Hippocates's great theorem, and what was it based on according to Dunham?

6. Explain in two sentences Euclid's method to prove the Pythagorean Theorem.

7. What did Dunham claim was Pythagoras's major contribution to geometry, and mathematical reasoning?

8. Describe who was Archimedes and how Dunham described his character.

9. Explain who was Hippocrates, his contribution to mathematics, and how do we know about him?

10. Explain who was Gerolamo Cardano, and how did he become involved with the solution to the cubic.

(see the answer keys)

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