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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. Which of the following is true in modern math about twin primes?
(a) They are not considered whole numbers.
(b) They are infinite.
(c) Their sum is always another prime number.
(d) We don't know if they are finite or infinite.

2. 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 successively smaller circles inside circles until he realized all of their ratios of diameter to area were equal.
(d) By constructing multi-sided polygons inside and outside a circle and determining their perimeters.

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

4. When was the work of these early thinkers rediscovered again in history?
(a) In the Elizabethian age.
(b) In the Renaissance.
(c) In the 18th century.
(d) In the 20th century.

5. Besides being a mathematician, what else other work was Archimedes famous for?
(a) Artist and musician.
(b) Politician.
(c) Inventor and scientist.
(d) Doctor and writer,

Short Answer Questions

1. What shape was NOT demonstrated in the Elements as having a relationship to other shapes?

2. What instruments did the Greeks use to square a shape?

3. Dunham showed that Heron's proof could also be used as which of the following?

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

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

(see the answer key)

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