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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. After working on pi, what did Archimedes continue with in his study of mathematics?
(a) He studied the volume to surface area ratios of cubes.
(b) He studied the volume and surface area of spheres, cones, and cylinders.
(c) He studied the relationship of sine to cosine.
(d) He studied the relationship between ratios in triangles.

2. After Hippocrates, what shape did the Greeks attempt to square without success?
(a) Pentagon.
(b) Parallelogram.
(c) Hemisphere.
(d) Circle.

3. "Straight lines in the same plane that will never meet if extended forever" is a definition of what?
(a) Intersection.
(b) Parallel lines.
(c) 180 degree angle.
(d) Circle.

4. What did Dunham consider extraordinary about the Elements?
(a) The content was not based on previous authors' work.
(b) The content was totally unique.
(c) How Hippocrates ordered the book.
(d) How geometric proofs were presented.

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

Short Answer Questions

1. What did Ferdinand Lindeman prove in 1882?

2. What did the Pythagorean Theorem accomplish for mathematics?

3. What was the bases of Hippocrates's proof ?

4. What range of values did Archimedes determine for pi?

5. What did Gauss set out to prove?

(see the answer key)

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