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

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

3. Which shapes as described by Euclid, inspired the Greek philosopher Plato?
(a) Regular polyhedrons.
(b) Spheres and cones.
(c) Manifolds.
(d) Triangles.

4. What were the proofs in Elements based on?
(a) Basic definitions.
(b) Novel notions.
(c) Lindeman's method.
(d) Ancient greek geometry.

5. What name did Euclid give for numbers that could be divided by numbers other than themselves and one?
(a) Even numbers.
(b) Discrete numbers.
(c) Composite numbers.
(d) Perfect numbers.

Short Answer Questions

1. Which of the following was NOT one of the basic definitions in Elements?

2. Which of the following was one of Euclid's great theorems?

3. In general, what did Euclid's number theory describe?

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

5. As described by Dunham, what did Archimedes demonstrate first in his proof on pi?

(see the answer key)

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