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 Eratosthanes most famous for?
(a) He showed that there are no even prime numbers.
(b) He developed a way to navigate using logitude and latitude.
(c) He developed a simple way to find prime numbers and for determining the circumference of the Earth.
(d) He showed that the Earth must be a sphere.

2. What did Dunham claim about Archimedes's determination of a number value for pi?
(a) Archimedes's number was very good, considering he did not have a way to calculate square roots.
(b) Archimedes's number was not very accurate, considering the technology of his time.
(c) Archimedes's number was perfectly correct.
(d) Archimedes's number could have been better if he had understood Euclid's work better,

3. "Straight lines in the same plane that will never meet if extended forever" is a definition of what?
(a) 180 degree angle.
(b) Intersection.
(c) Circle.
(d) Parallel lines.

4. Which of the following could NOT be included as a step in Euclid's great theorem?
(a) If a new number is found to be composite, then it must have some prime as a divisor.
(b) Divide a infinite group of primes by the sum of their composites.
(c) Take a finite group of primes and add them together, plus one.
(d) After summation, the new number can be prime or composite.

5. Which mathematician was first to take the challenge to solve cubic equations?
(a) Luca Pacioli.
(b) Tartaglia.
(c) Scipione del Ferro.
(d) Niccolo Fontana.

Short Answer Questions

1. Who was del Ferro's student?

2. What did the Pythagorean Theorem accomplish for mathematics?

3. What name did Euclid give for numbers that could be divided by numbers other than themselves and one?

4. How do we know about Hippocrates proofs and theorems?

5. Who was Eratosthanes?

Short Essay Questions

1. Why did Euclid's postulate on parallel lines trouble mathematicians for centuries?

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

3. How many definitions were in Euclid's book? List some of the definitions he included.

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

5. What did Dunham explain about the shift in learning from the West to the East?

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

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

8. Describe in two sentences Archimedes's method for determining circular area.

9. 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.

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

(see the answer keys)

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