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 is the name for determining the area of an enclosed space by constructing a square of equivalent area?
(a) Cubation.
(b) Quadrature.
(c) Square root.
(d) Triangulation.

2. Which of the following was NOT one of Gauss' discoveries?
(a) That under Euclid's definition parallel lines can intersect.
(b) "Non-euclidean" geometry.
(c) That angles in a triangles can not add up to more than 180 degrees.
(d) That there is no apparent contraction to the assumption that the sum of angles in a triangle can have fewer than 180 degrees.

3. What did Euclid do in his 48th proposition?
(a) Euclid proved the Pythagorean Theorem.
(b) Euclid proved the converse of the Pythagorean Theorem.
(c) Euclid demonstrated how to use the Pythagorean Theorem.
(d) Euclid demonstrated the faults of the Pythagorean Theorem.

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

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

Short Answer Questions

1. Who asked Tartaglia for his solution to cubic equations?

2. What did Dunham discuss for many pages in this chapter?

3. Which of the following is INCORRECT, and not used in Archimedes proof of his theory?

4. What else, besides a solution to cubic equations, was in Cardano's book?

5. How many sides did the pentadecagon have, as presented by Euclid?

Short Essay Questions

1. Describe what is quadrature and why it was useful in the time of Hippocrates.

2. Describe Lindeman's work on the square of a circle, and state what he discovered.

3. What did Dunham describe in the epilogue of the chapter?

4. Explain why Archimedes finding a number value for pi was considered a great achievement according to Dunham.

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

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

7. Describe the contents of Cardano's book.

8. Describe who was Archimedes and how Dunham described his character.

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

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

(see the answer keys)

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