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 the bases of Hippocrates's proof ?
(a) Properties of points and lines.
(b) Properties of triangles and semicircles.
(c) Properties of squares and cubes.
(d) Properties of area to volume measurements.

2. Which of the following best describes Cardano's character?
(a) Religious.
(b) Eccentric.
(c) Arrogant.
(d) Flirtacious.

3. After working on pi, what did Archimedes continue with in his study of mathematics?
(a) He studied the volume and surface area of spheres, cones, and cylinders.
(b) He studied the relationship of sine to cosine.
(c) He studied the relationship between ratios in triangles.
(d) He studied the volume to surface area ratios of cubes.

4. What instruments did the Greeks use to square a shape?
(a) A compass and a ruled straight-edge.
(b) A small grid.
(c) A pendulum.
(d) A sphere and ruler.

5. 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) "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) "The inverse of a line makes a circle."

Short Answer Questions

1. Dunham showed that Heron's proof could also be used as which of the following?

2. What was the title of Cardano's book which contained the solution to the cubic?

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

4. Where was Archimedes born?

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

Short Essay Questions

1. Describe what mathematical and artistic movements are focused on in the second half of the 19th century.

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

3. Where did the center of mathematical thinking shift to in the !7th Century, and who are the major scholars of this time period?

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. Describe the great theorem explained by Dunham in this chapter.

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

8. Who was Heron, and what is known about him today?

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

10. Describe what Gauss discovered according to Dunham.

(see the answer keys)

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