Journey Through Genius: The Great Theorems of Mathematics Quiz | Four Week Quiz A

William Dunham (mathematician)
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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 Dunham, what did Archimedes demonstrate first in his proof on pi?
(a) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's circumference.
(b) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's diameter and the other leg equal to the circle's circumference.
(c) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's diameter.
(d) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's hypotenuse and the other leg equal to the circle's circumference.

2. What did Euclid state about pi in Elements?
(a) The proportion of diameter to area is never equal.
(b) There is a constant relationship between the area of a circle and the square of its diameter.
(c) There is no relationship between the area of a circle and its circumference.
(d) The proportion of area to circumference is never equal.

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

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

5. What did Dunham claim about Archimedes's determination of a number value for pi?
(a) Archimedes's number was very good, considering he did not have a way to calculate square roots.
(b) Archimedes's number was not very accurate, considering the technology of his time.
(c) Archimedes's number was perfectly correct.
(d) Archimedes's number could have been better if he had understood Euclid's work better,

Short Answer Questions

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

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

3. Which words best describe how solid proofs were developed in Elements?

4. What did Plato use his inspiration from Euclid for?

5. Which of Euclid's postulates troubled many of the following generations of mathematicians?

(see the answer key)

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