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. Which of Euclid's postulates troubled many of the following generations of mathematicians?
(a) Euclid's postulate on parallel lines.
(b) Euclid's postulate on creating an arc.
(c) Euclid's proof on right triangles.
(d) Euclid's postulate on right triangles.

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

3. Which was true of Euclid's number theory?
(a) It was incorrect, as proved by Plato.
(b) It has an impact on modern math.
(c) It has been proven too basic to be useful.
(d) It was proven to the true by Hippocrates.

4. Where did Hippocrates come from?
(a) Constinople.
(b) Chios.
(c) Rome.
(d) Athens.

5. Heron's work referred to the work of what other famous scholar?
(a) Thales.
(b) Euclid.
(c) Hippocrates.
(d) Archimedes.

Short Answer Questions

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

2. What did Archimedes manage to prove using Euclid's ideas?

3. Which words best describe how solid proofs were developed in Elements?

4. What was most useful about finding the square of a shape, before Hippocrates?

5. Which of the following was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?

Short Essay Questions

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

2. What were the two transfinite cardinals discovered by Cantor, and what method did he use to determine them?

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

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

5. What was already known about circles before Archimedes?

6. Describe the connection between Fermat and Euler's work.

7. Describe the contents of Cardano's book.

8. Explain who was Hippocrates, his contribution to mathematics, and how do we know about him?

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

10. Give an example of a series who's sum is still unknown.

(see the answer keys)

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