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

2. That properties of specific shapes were early Egyptians aware of?
(a) Right triangles.
(b) Pi and the diameter of a circle.
(c) Irregular solids.
(d) Parallelograms.

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

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

5. Why did Cardano take an oath to secrecy?
(a) It was the only way to get his book published.
(b) It was the only way he could become a priest,
(c) It was to the only way to win the contest with Fior,
(d) It was the only way to get Tartaglia's solution to cubic equations.

Short Answer Questions

1. What shape was NOT demonstrated in the Elements as having a relationship to other shapes?

2. What did Dunham claim about Archimedes's determination of a number value for pi?

3. Where was Archimedes born?

4. What was true about Hippocrates's proof?

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

Short Essay Questions

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

2. Explain what Neils Abel proved.

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

4. Describe Euclid's postulates and notions in how they were important in constructing his proofs.

5. How many definitions were in Euclid's book? List some of the definitions he included.

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

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

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

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

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

(see the answer keys)

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