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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?

This section contains 488 words(approx. 2 pages at 300 words per page) |