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

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

**3. What was Euclid's definition of a prime number?**
**(a)** Numbers which do not, and can not, contain a perfect number. **(b)** Numbers which are divisible by 2. **(c)** Numbers which can only be divided by themselves and 1. **(d)** Numbers which contain an infinite number of composite numbers.

**4. Which of the following is false about the modern implications of Euclid's number theory?**
**(a)** Euclid gave a good idea for how to construct even perfect numbers. **(b)** Whether there are no odd perfect numbers is still not known. **(c)** Great mathematicians continue to puzzle over some aspects of Euclid's number theory. **(d)** Euclid's recipe for constructing even perfect numbers is incorrect.

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

## Short Answer Questions

**1.** What name did Euclid give for numbers that could be divided by numbers other than themselves and one?

**2.** Which of the following is true in modern math about twin primes?

**3.** According to Euclid, when is a triangle a right triangle?

**4.** How did Lindeman prove his conclusion?

**5.** Which of the following was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?

This section contains 485 words(approx. 2 pages at 300 words per page) |