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 was the same about Apollonius and Erosthanes?
(a) They were both mathematicians.
(b) They both studied the Universe.
(c) They were both born in the same year.
(d) They both calculated the circumference of the earth.

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

3. Which of the following was an important proposition given by Euclid's number theory?
(a) Any perfect number is divisible by some composite number.
(b) Any even number is divisible by 3.
(c) Numbers from one to ten are only divisible by composite numbers.
(d) Any composite number is divisible by some prime number.

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

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

Short Answer Questions

1. Who challenged Tartaglia to a contest to solve cubic equations?

2. Who was Neil's Abel?

3. Which was true of Euclid's number theory?

4. That properties of specific shapes were early Egyptians aware of?

5. As described by Dunham, what did Archimedes demonstrate first in his proof on pi?

Short Essay Questions

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

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

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

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

7. Explain some puzzles suggested by Euclid's theories.

8. Explain when the knowledge of ancient scholars was rediscovered.

9. Describe the events that follow del Ferro's death between Fior and Tartaglia.

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

(see the answer keys)

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