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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 was a major part of Gauss' work in mathematics?
(a) Proofs to show that Archimedes' number theory was wrong.
(b) Proofs on the area of a square.
(c) Elemental proofs related to the foundations of algebra.
(d) Simple proofs to demonstrate Bernoulli's series.

2. What did Euclid state about pi in Elements?
(a) There is no relationship between the area of a circle and its circumference.
(b) There is a constant relationship between the area of a circle and the square of its diameter.
(c) The proportion of area to circumference is never equal.
(d) The proportion of diameter to area is never equal.

3. What did the Pythagorean Theorem accomplish for mathematics?
(a) The ability to find square roots.
(b) The concept of constructing useful mathematics.
(c) The concept of providing a logical proof.
(d) The ability to measure angles.

4. What was true about Heron's theorem as described by Dunham?
(a) It was to find the area of a triangle when only the length of the sides are known.
(b) It was to solve equations were only two varibles are known.
(c) It was to determine the area of a circle by measuring a right triangle inside the circle.
(d) It was to determine the volume of a sphere without measuring the circumference.

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

Short Answer Questions

1. What did most of 19th century mathematics focus on, as highlighted by Dunham?

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

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

4. What was Eratosthanes most famous for?

5. What series was Euler most famous for?

(see the answer key)

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