Journey Through Genius: The Great Theorems of Mathematics Quiz | Eight Week Quiz D

William Dunham (mathematician)
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This quiz consists of 5 multiple choice and 5 short answer questions through Cardano and the Solution of the Cubic.

Multiple Choice Questions

1. As described by Dunham, what did Archimedes demonstrate first in his proof on pi?
(a) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's hypotenuse and the other leg equal to the circle's circumference.
(b) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's diameter.
(c) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's circumference.
(d) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's diameter and the other leg equal to the circle's circumference.

2. Which of the following could NOT be included as a step in Euclid's great theorem?
(a) Divide a infinite group of primes by the sum of their composites.
(b) If a new number is found to be composite, then it must have some prime as a divisor.
(c) Take a finite group of primes and add them together, plus one.
(d) After summation, the new number can be prime or composite.

3. What shape was NOT demonstrated in the Elements as having a relationship to other shapes?
(a) Hexagon.
(b) Hyperbola.
(c) Pentagon.
(d) Triangle.

4. What did Ferdinand Lindeman prove in 1882?
(a) It is possible to find the square of a circle.
(b) It is impossible to find the square of a semicircle.
(c) That the square root of the hypotenuse of a right triangle can not be found.
(d) That the square of a circle can not be found with a compass and a straight-edge.

5. How did Archimedes demonstrate his theory of pi?
(a) He demonstrated that the area of the circle is always greater than the area of the triangle.
(b) He demonstrated that the area of the circle is never equal to the area of the triangle.
(c) He demonstrated that the area of the circle is never less than the area of the triangle.
(d) He demonstrated that the area of the circle is neither greater than nor less than the area of the triangle and therefore must be equal to it.

Short Answer Questions

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

2. When was the work of these early thinkers rediscovered again in history?

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

4. What did Archimedes manage to prove using Euclid's ideas?

5. Which of the following is true in modern math about twin primes?

(see the answer key)

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