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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. Which of the following is INCORRECT, and not used in Archimedes proof of his theory?
(a) 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.
(b) 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.
(c) The area of a triangle is one half the base times the height.
(d) Since the circumference can also be expressed as twice the radius multiplied by π, the area is 2πr²/2, or πr².
2. What was aleph naught?
(a) A method to determine the sum of a series.
(b) A symbol to represent the number of items in a set.
(c) A symbol to state the sum of a series.
(d) A method to numerate terms.
3. Where was the modern number system developed?
(a) In the West.
(b) In ancient Rome.
(c) In the East.
(d) In ancient Alexanderia.
4. What did Gauss set out to prove?
(a) That the sum of the angles in a triangle is 180 degrees.
(b) That a circle can have less than 360 degrees.
(c) That a right angle is always equal to 90 degrees.
(d) That Euclid's postulate on straight lines was incorrect.
5. Which of the following was NOT one of Gauss' discoveries?
(a) That angles in a triangles can not add up to more than 180 degrees.
(b) That under Euclid's definition parallel lines can intersect.
(c) "Non-euclidean" geometry.
(d) That there is no apparent contraction to the assumption that the sum of angles in a triangle can have fewer than 180 degrees.
Short Answer Questions
1. Where does the center of mathematical thinking shift to after Italy?
2. What was Euclid's definition of a prime number?
3. Which phrase best describes Newton as a student at Cambridge?
4. Which of the following is true about pi, as described by Dunham.
5. How do we know about Hippocrates proofs and theorems?
This section contains 464 words
(approx. 2 pages at 300 words per page)