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 is a "depressed cubic"?
(a) A method to simplify measuring complex geometric forms.
(b) A method to simpify the x squared value in a cubic equation.
(c) A method to solve equations with two variables.
(d) A method to logically square all the factors in a cubic equation.

2. Besides being a mathematician, what else other work was Archimedes famous for?
(a) Inventor and scientist.
(b) Politician.
(c) Doctor and writer,
(d) Artist and musician.

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

4. Who was Neil's Abel?
(a) He demonstrated the modern version of the Pythagorean Theorem.
(b) He proved that quintic equations cannot be solved using algebra.
(c) He demonstrated that Cardano's solution to the cubic was incorrect,
(d) He proved that to solve a quartic equation, one must use more than algebra.

5. What did Dunham claim about Archimedes's determination of a number value for pi?
(a) Archimedes's number could have been better if he had understood Euclid's work better,
(b) Archimedes's number was not very accurate, considering the technology of his time.
(c) Archimedes's number was perfectly correct.
(d) Archimedes's number was very good, considering he did not have a way to calculate square roots.

Short Answer Questions

1. Who was del Ferro's student?

2. What is true about prime numbers?

3. Exactly what limit is reached at a quartic equation?

4. What is the name for determining the area of an enclosed space by constructing a square of equivalent area?

5. How did Archimedes demonstrate his theory of pi?

Short Essay Questions

1. What did Dunham explain about the shift in learning from the West to the East?

2. What did Dunham claim was Pythagoras's major contribution to geometry, and mathematical reasoning?

3. Explain who was Hippocrates, his contribution to mathematics, and how do we know about him?

4. Explain in two sentences Euclid's method to prove the Pythagorean Theorem.

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

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

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

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

9. What did Dunham describe in the epilogue of the chapter?

10. Describe the contents of Cardano's book.

(see the answer keys)

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