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 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 area of a circle and the square of its diameter is really the same as the relationship of diameter to circumference.
(d) That the square of a diameter is equal to pi.

2. How many sides did the pentadecagon have, as presented by Euclid?
(a) Ten.
(b) Fifteen.
(c) Twenty.
(d) Five.

3. What did Hippocrates do that advanced mathematical methods?
(a) He created a new ways to disprove theories.
(b) He demonstrated that geometry does not have to be based on previous knowledge.
(c) He proved that mathematics can be applied in a unlogical order.
(d) He built theorems based on sequencially more complex proofs.

4. Which of Euclid's postulates troubled many of the following generations of mathematicians?
(a) Euclid's proof on right triangles.
(b) Euclid's postulate on right triangles.
(c) Euclid's postulate on creating an arc.
(d) Euclid's postulate on parallel lines.

5. Which is a geometric concept that humans have been aware of since the dawn of agriculture?
(a) Volume.
(b) Area.
(c) Gravity.
(d) Metric system.

Short Answer Questions

1. What was true about Heron's theorem as described by Dunham?

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

3. Exactly what limit is reached at a quartic equation?

4. Who was the first of ancient philosophers to consider why geometric properties existed?

5. As described by Archimedes, what is always true about he diameter of the circle?

Short Essay Questions

1. Explain what Archimedes went on to study after the circle, and what was Dunham's opinion of this work.

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

3. Describe why Dunham infers that Euclid's Elements was an evolutionary book not so much for what it said, but in how it was presented.

4. Who was Heron, and what is known about him today?

5. What did Dunham describe in the epilogue of the chapter?

6. Who was Luca Pacioli, and what controversy was sparked over his writings?

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

8. Describe what is quadrature and why it was useful in the time of Hippocrates.

9. According the Dunham, how did Euclid prove his theory on the infinitude of primes?

10. Describe what work of Euclid's fascinated Plato and his theory on the shape of the Universe.

(see the answer keys)

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