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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. As described by Archimedes, what is always true about he diameter of the circle?
(a) It's equal to pi.
(b) It's equal to the square of the radius.
(c) It's never proportional to its circumference.
(d) It's always proportional to its circumference.

2. What shape was NOT demonstrated in the Elements as having a relationship to other shapes?
(a) Triangle.
(b) Hyperbola.
(c) Hexagon.
(d) Pentagon.

3. In what century did Archimedes live?
(a) Third century B.C.
(b) Nineteeth century A.D.
(c) First century A.D,
(d) Twelthf century A.D.

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

5. How did Lindeman prove his conclusion?
(a) Lindeman proved that square roots are irrational numbers.
(b) Lindeman proved that some numbers are not constructable with only a compass and straight-edge.
(c) Lindeman proved that all numbers are constructable with a compass and ruler.
(d) Lindeman proved that some numbers are constructable without the use of a compass.

Short Answer Questions

1. How do we know about Hippocrates proofs and theorems?

2. Which of the following is an example of a perfect number?

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

4. According to Euclid, when is a triangle a right triangle?

5. What was most useful about finding the square of a shape, before Hippocrates?

(see the answer key)

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