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

2. Which shapes as described by Euclid, inspired the Greek philosopher Plato?
(a) Spheres and cones.
(b) Regular polyhedrons.
(c) Manifolds.
(d) Triangles.

3. What did Heron's advances put into historical perspective for Dunham?
(a) A shift in information flow that ignored socioeconomic order.
(b) A change in political theory across the globe.
(c) A shift in learning across continents.
(d) A change in learning foundations in the ancient scholarly universities.

4. Numbers whose divisor add up to itself, was considered which type of number according to Euclid?
(a) Even number.
(b) Perfect number.
(c) Composite number.
(d) Nominal number.

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

Short Answer Questions

1. Who's method did Tartaglia's challenger use in the contest to solve cubic equations?

2. Which of the following is false about the modern implications of Euclid's number theory?

3. Which of the following was one of Euclid's great theorems?

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

5. What was Hippocrates's great advance to mathematics?

Short Essay Questions

1. What did Euclid state for his theory on prime numbers?

2. Describe the ancient city Alexandria and name a few of its third century geniuses.

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

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

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

6. Explain what Neils Abel proved.

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

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

9. Describe what the Egyptians knew about geometry and triangles before Hippocrates.

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

(see the answer keys)

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