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. According to Euclid, when is a triangle a right triangle?
(a) When a triangle can be constructed with three unequal sides.
(b) When a triangle does not have a side which can be considered a hypotenuse.
(c) When a triangle has three sides whose squares are equal to the area of the triangle.
(d) When a triangle has a side whose square is the sum of the squares of the two legs.

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

3. What did Dunham discuss for many pages in this chapter?
(a) Heron's complicated proof.
(b) Heron's political tendancy.
(c) Heron's origins of the universe.
(d) Heron's religious beliefs-

4. What did the Pythagorean Theorem accomplish for mathematics?
(a) The concept of providing a logical proof.
(b) The ability to measure angles.
(c) The ability to find square roots.
(d) The concept of constructing useful mathematics.

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

Short Answer Questions

1. Which of the following best describes Archimedes as discussed by Dunham?

2. What did Dunham consider as Archimedes's "masterpiece"?

3. Which is a geometric concept that humans have been aware of since the dawn of agriculture?

4. Which of the following is true about pi, as described by Dunham.

5. Besides being a mathematician, what else other work was Archimedes famous for?

Short Essay Questions

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

2. Describe Euclid's postulates and notions in how they were important in constructing his proofs.

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

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

5. How did Heron find the area of a triangle, and what did Dunham state about Heron's work?

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

7. What was already known about circles before Archimedes?

8. Describe Euclid's definition of prime numbers and the relationship he stated as existing between prime and composite numbers.

9. Describe how Cardano eventually publishes the solution to cubic equations.

10. 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.

(see the answer keys)

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