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 did Lindeman prove his conclusion?
(a) Lindeman proved that square roots are irrational numbers.
(b) Lindeman proved that some numbers are not constructable with only a compass and straight-edge.
(c) Lindeman proved that some numbers are constructable without the use of a compass.
(d) Lindeman proved that all numbers are constructable with a compass and ruler.

2. Which of the following becomes an important definition in mathematics that was first presented in Elements?
(a) Parallel line.
(b) 180 degree angle.
(c) Intersection.
(d) Circle.

3. Who wrote a treatise that supposed that cubic equations may be impossible to solve?
(a) Scipione del Ferro.
(b) Luca Pacioli.
(c) Niccolo Fontana.
(d) Gerolamo Cardano.

4. Who was the first of ancient philosophers to consider why geometric properties existed?
(a) Thales.
(b) Hippocrates.
(c) Aristotle.
(d) Pythagoras.

5. Which is a geometric concept that humans have been aware of since the dawn of agriculture?
(a) Gravity.
(b) Area.
(c) Volume.
(d) Metric system.

Short Answer Questions

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

2. As described by Dunham, what did Archimedes demonstrate first in his proof on pi?

3. What were the proofs in Elements based on?

4. What was the bases of Hippocrates's proof ?

5. How many definitions were stated in Elements?

Short Essay Questions

1. Describe what work of Euclid's fascinated Plato and his theory on the shape of the Universe.

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

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

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

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

6. Describe what the Egyptians knew about geometry and triangles before Hippocrates.

7. Describe the ancient city Alexandria and name a few of its third century geniuses.

8. Describe what Gauss discovered according to Dunham.

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

10. Describe the contents of Cardano's book.

(see the answer keys)

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