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

2. Which of the following was NOT defined by Euclid?
(a) Nominal numbers.
(b) Whole numbers.
(c) Even numbers.
(d) Odd numbers.

3. What did Gauss set out to prove?
(a) That a circle can have less than 360 degrees.
(b) That a right angle is always equal to 90 degrees.
(c) That Euclid's postulate on straight lines was incorrect.
(d) That the sum of the angles in a triangle is 180 degrees.

4. Which is one of the common notions presented in Elements?
(a) "The inverse of a line makes a circle."
(b) "Things with are equal have an inverse that is equal."
(c) "Points with equal values can be connected with a line of equal value."
(d) "Things which are equal to the same thing are also equal to each other."

5. Who was del Ferro's student?
(a) Gerolamo Cardano.
(b) Niccolo Fontana.
(c) Luca Pacioli.
(d) Antonio Fior.

Short Answer Questions

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

2. In what time period did mathematicians find a solution to cubic equations?

3. Who acted as the gate keepers of knowledge?

4. What allowed Cardano to justify publishing his book?

5. What instruments did the Greeks use to square a shape?

Short Essay Questions

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

2. What was Euclid's definition of composite and perfect numbers?

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

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

5. 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.

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

7. What was already known about circles before Archimedes?

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

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

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

(see the answer keys)

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