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 range of values did Archimedes determine for pi?
(a) Between 3 10/11 and 3 1/7.
(b) Between 3 and 4.
(c) Between 3 1/2 and 3 5/8.
(d) Between 3 and 3 1/2.

2. After Hippocrates, what shape did the Greeks attempt to square without success?
(a) Pentagon.
(b) Parallelogram.
(c) Hemisphere.
(d) Circle.

3. Which city was the center of thinking and learning in Third century BC?
(a) Athens.
(b) Olympia.
(c) Alexandria.
(d) Rome.

4. What was Hippocrates's great advance to mathematics?
(a) He showed how to find the angles in a right triangle.
(b) He showed how to square a circle.
(c) He showed how to square a figure with curved sides.
(d) He showed how to simplify the area of a triangle.

5. What provided most of the content in the book Elements?
(a) Postulates.
(b) Hypotheses.
(c) Notions.
(d) Propositions.

Short Answer Questions

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

2. Who was Eratosthanes?

3. What did Apollonius work with in mathematics?

4. What did Dunham consider as Archimedes's "masterpiece"?

5. Besides being a mathematician, what else other work was Archimedes famous for?

Short Essay Questions

1. Explain who was Gerolamo Cardano, and how did he become involved with the solution to the cubic.

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

3. Describe what Gauss discovered according to Dunham.

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

5. Explain what Neils Abel proved.

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

7. Describe the contents of Cardano's book.

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

9. According the Dunham, how did Euclid prove his theory on the infinitude of primes?

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

(see the answer keys)

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