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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. How did Archimedes demonstrate his theory of pi?
(a) He demonstrated that the area of the circle is never equal to the area of the triangle.
(b) He demonstrated that the area of the circle is never less than the area of the triangle.
(c) He demonstrated that the area of the circle is always greater 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.

2. What did Dunham discuss for many pages in this chapter?
(a) Heron's religious beliefs-
(b) Heron's political tendancy.
(c) Heron's origins of the universe.
(d) Heron's complicated proof.

3. What did Cantor's beliefs lead him to think?
(a) That he was seeing God when he worked on equations.
(b) That he was tapping into the nature of God by delving into the infinite.
(c) That he was learning about the origins of God.
(d) That he was God.

4. What is true about real numbers between 0 and 1?
(a) They are denumerable,
(b) They are not denumerable.
(c) No sum can be determined.
(d) There is no set for these numbers.

5. Which of the following becomes an important definition in mathematics that was first presented in Elements?
(a) Intersection.
(b) Parallel line.
(c) 180 degree angle.
(d) Circle.

Short Answer Questions

1. After Hippocrates, what shape did the Greeks attempt to square without success?

2. Which of the following was one of Gauss' early discoveries?

3. What is true about prime numbers?

4. What did Dunham consider as Archimedes's "masterpiece"?

5. What was aleph naught?

(see the answer key)

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