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 allowed Cardano to justify publishing his book?
(a) He found del Ferro's orgininal solution to the cubic.
(b) He was dead, and the book was really published by his student.
(c) He found Fior's documents which spoke against Tartaglia.
(d) He was punished as a heretic,

2. What did Euclid state about pi in Elements?
(a) There is a constant relationship between the area of a circle and the square of its diameter.
(b) There is no relationship between the area of a circle and its circumference.
(c) The proportion of diameter to area is never equal.
(d) The proportion of area to circumference is never equal.

3. Heron devised which of the following methods?
(a) A way to determine the volume in a sphere.
(b) A way to determine the area of a triangle.
(c) A way to solve binomial equations.
(d) A way to apply mathematics to public health.

4. Heron's work referred to the work of what other famous scholar?
(a) Hippocrates.
(b) Thales.
(c) Euclid.
(d) Archimedes.

5. According to Euclid, when is a triangle a right triangle?
(a) When a triangle can be constructed with three unequal sides.
(b) When a triangle has three sides whose squares are equal to the area of the triangle.
(c) When a triangle has a side whose square is the sum of the squares of the two legs.
(d) When a triangle does not have a side which can be considered a hypotenuse.

Short Answer Questions

1. What did Gauss set out to prove?

2. How many definitions were stated in Elements?

3. How do we know about Hippocrates proofs and theorems?

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

5. Which of the following best describes Cardano's character?

Short Essay Questions

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

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

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

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

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

6. Describe the contents of Cardano's book.

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

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

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

10. Describe what Gauss discovered according to Dunham.

(see the answer keys)

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