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This quiz consists of 5 multiple choice and 5 short answer questions through Cantor and the Transfinite Realm.

## Multiple Choice Questions

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

**2. Where did Newton go to school before he went to Cambridge?**
**(a)** Cambridge Prep. **(b)** Charles II Grammar School. **(c)** Oxford Grammar School. **(d)** The King's School.

**3. How did Cantor finally prove his theory?**
**(a)** By refining and expanding set theory. **(b)** By extension of the Pythagorean Theorem. **(c)** By using basic algebra. **(d)** By extension of the infinite series.

**4. How did Archimedes arrive at a number value for pi?**
**(a)** By proving pi could not be equal to one. **(b)** By constructing multi-sided polygons inside and outside a circle and determining their perimeters. **(c)** By proving that pi could not be a negative number. **(d)** By constructing successively smaller circles inside circles until he realized all of their ratios of diameter to area were equal.

**5. Which of the following is INCORRECT, and not used in Archimedes proof of his theory?**
**(a)** The area of a triangle is one half the base times the height. **(b)** Since the base of the triangle is equal to the circumference and the height is the radius, the area of the triangle in his proof is 1/2 the radius times the circumference. **(c)** Since the circumference can also be expressed as twice the radius multiplied by π, the area is 2πr²/2, or πr². **(d)** Since the diameter of a circle is equal to the hypotenuse of the right triangle, the area of the triangle in his proof is 1/2 the radius times the circumference.

## Short Answer Questions

**1.** What did George Cantor discover?

**2.** What was the title of Cardano's book which contained the solution to the cubic?

**3.** Which of the following is an example of a postulate that must be accepted in Elements?

**4.** Which of the following becomes an important definition in mathematics that was first presented in Elements?

**5.** What did Ferdinand Lindeman prove in 1882?

This section contains 468 words(approx. 2 pages at 300 words per page) |