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This quiz consists of 5 multiple choice and 5 short answer questions through Heron's Formula for Triangular Area.

Multiple Choice Questions

1. How did Archimedes arrive at a number value for pi?
(a) By proving pi could not be equal to one.
(b) By proving that pi could not be a negative number.
(c) By constructing multi-sided polygons inside and outside a circle and determining their perimeters.
(d) By constructing successively smaller circles inside circles until he realized all of their ratios of diameter to area were equal.

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

3. What was true about Hippocrates's proof?
(a) It was useful for circles.
(b) The proof was easy if their was advanced technology available.
(c) The proof was exceedingly difficult and not understood at the time.
(d) It was fairly easy and simple.

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

5. Which of the following is true about pi, as described by Dunham.
(a) The measurement of pi is no longer a mystery as we have an exact number value in modern mathematics.
(b) The measurement of pi should not have been so difficult for Archimedes to demonstrate.
(c) The measurement of pi is a challenge that continues into modern mathematics.
(d) The measurement of pi was redetermined after Archimedes's death.

Short Answer Questions

1. Which was true of Euclid's number theory?

2. What did Apollonius work with in mathematics?

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

4. Besides being a mathematician, what else other work was Archimedes famous for?

5. Numbers whose divisor add up to itself, was considered which type of number according to Euclid?

(see the answer key)

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