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 do we know in modern times about Heron?
(a) We know very little, but much of his work survives.
(b) We know he lived in Rome.
(c) We know he was a teacher and philosopher but much of his work has been lost.
(d) We know he was an influencial scholar, but we don't know who his students were.

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

3. What was the title of Cardano's book which contained the solution to the cubic?
(a) Tarsisia.
(b) Ars Magna.
(c) La Magnifica.
(d) Elements.

4. Which of the following was NOT defined by Euclid?
(a) Nominal numbers.
(b) Even numbers.
(c) Odd numbers.
(d) Whole numbers.

5. What did the Pythagorean Theorem accomplish for mathematics?
(a) The ability to measure angles.
(b) The concept of constructing useful mathematics.
(c) The ability to find square roots.
(d) The concept of providing a logical proof.

Short Answer Questions

1. Who wrote a treatise that supposed that cubic equations may be impossible to solve?

2. What provided most of the content in the book Elements?

3. Which mathematician was first to take the challenge to solve cubic equations?

4. What is a "depressed cubic"?

5. What was known about pi, during Archimedes' time?

Short Essay Questions

1. Describe why Dunham infers that Euclid's Elements was an evolutionary book not so much for what it said, but in how it was presented.

2. Describe the contents of Cardano's book.

3. Describe the events that follow del Ferro's death between Fior and Tartaglia.

4. Explain what Archimedes went on to study after the circle, and what was Dunham's opinion of this work.

5. Describe in two sentences Archimedes's method for determining circular area.

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

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

8. What was already known about circles before Archimedes?

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

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

(see the answer keys)

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