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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. How many sides did the pentadecagon have, as presented by Euclid?**
**(a)** Twenty. **(b)** Five. **(c)** Ten. **(d)** Fifteen.

**2. Which of the following is an example of a perfect number?**
**(a)** 10. **(b)** 6. **(c)** 20. **(d)** 1.

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

**4. Which of the following was NOT defined by Euclid?**
**(a)** Even numbers. **(b)** Nominal numbers. **(c)** Odd numbers. **(d)** Whole numbers.

**5. Which of the following was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?**
**(a)** Euclid used propositions about similar angles and parallel lines. **(b)** Euclid constructed squares on the sides of right triangles. **(c)** Euclid used his own axioms and propositions to show relationships, **(d)** Euclid stated that the diagonal hypotenuse of a right triangle is equal to the sums of the squares of the two legs.

## Short Answer Questions

**1.** After working on pi, what did Archimedes continue with in his study of mathematics?

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

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

**4.** What did Dunham claim about Archimedes's determination of a number value for pi?

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

This section contains 393 words(approx. 2 pages at 300 words per page) |