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This quiz consists of 5 multiple choice and 5 short answer questions through Archimedes' Determination of Circular Area.

Multiple Choice Questions

1. What provided most of the content in the book Elements?
(a) Propositions.
(b) Postulates.
(c) Hypotheses.
(d) Notions.

2. How many definitions were stated in Elements?
(a) Five.
(b) Thirty.
(c) Eighteen.
(d) Twenty-three.

3. 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 square of a diameter is equal to pi.
(d) That the area of a circle and the square of its diameter is really the same as the relationship of diameter to circumference.

4. Which of Euclid's postulates troubled many of the following generations of mathematicians?
(a) Euclid's postulate on creating an arc.
(b) Euclid's proof on right triangles.
(c) Euclid's postulate on right triangles.
(d) Euclid's postulate on parallel lines.

5. What did Dunham claim about Archimedes's determination of a number value for pi?
(a) Archimedes's number was perfectly correct.
(b) Archimedes's number was very good, considering he did not have a way to calculate square roots.
(c) Archimedes's number could have been better if he had understood Euclid's work better,
(d) Archimedes's number was not very accurate, considering the technology of his time.

Short Answer Questions

1. What did Gauss set out to prove?

2. Which of the following is true about pi, as described by Dunham.

3. What did Euclid do in his 48th proposition?

4. Who was the author of the book Elements?

5. How did Archimedes arrive at a number value for pi?

(see the answer key)

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