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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?

This section contains 532 words(approx. 2 pages at 300 words per page) |