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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 did Cantor find after extending the continuum between 0 and 1 into two dimensions?
(a) That the set is still equal to c.
(b) That the series is infinite.
(c) That the set is equal to 1.
(d) That the set is infinite.

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

3. That properties of specific shapes were early Egyptians aware of?
(a) Parallelograms.
(b) Pi and the diameter of a circle.
(c) Right triangles.
(d) Irregular solids.

4. What did Archimedes manage to prove using Euclid's ideas?
(a) That the relationship of area to circumference is really the same as the relationship of radius to diameter.
(b) That the value of pi is proportional to the area of the circle.
(c) That the area of a circle and the square of its diameter is really the same as the relationship of diameter to circumference.
(d) That the square of a diameter is equal to pi.

5. What did Cantor's work do to mathematics?
(a) It forced the reexamination of set theory.
(b) It caused much agreement among mathematicians on the use of calculus.
(c) It caused a reevaluation of basic algebra.
(d) It raised arguments on the origins of geometry.

Short Answer Questions

1. As described by Archimedes, what is always true about he diameter of the circle?

2. Who was the first of ancient philosophers to consider why geometric properties existed?

3. What did Dunham describe as the same between artistic movements and mathematical studies in the 19th century?

4. How did Archimedes demonstrate his theory of pi?

5. What did Gauss do with his best work?

(see the answer key)

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