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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)