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This quiz consists of 5 multiple choice and 5 short answer questions through A Sampler of Euler's Number Theory.

## Multiple Choice Questions

**1. How did Archimedes arrive at a number value for pi?**
**(a)** By proving that pi could not be a negative number. **(b)** By constructing multi-sided polygons inside and outside a circle and determining their perimeters. **(c)** By proving pi could not be equal to one. **(d)** By constructing successively smaller circles inside circles until he realized all of their ratios of diameter to area were equal.

**2. 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 diameter. **(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 circumference. **(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.

**3. Exactly what limit is reached at a quartic equation?**
**(a)** The limit of algebra. **(b)** The limit of logical geometric proofs. **(c)** The limit of the decompressed cubic method. **(d)** The limit of the Pythagorean Theorem.

**4. Who acted as the gate keepers of knowledge?**
**(a)** Greek philosophers. **(b)** Arabian scholars. **(c)** Roman emporers. **(d)** Greek tradesman.

**5. What was true about Heron's theorem as described by Dunham?**
**(a)** It was to determine the area of a circle by measuring a right triangle inside the circle. **(b)** It was to determine the volume of a sphere without measuring the circumference. **(c)** It was to find the area of a triangle when only the length of the sides are known. **(d)** It was to solve equations were only two varibles are known.

## Short Answer Questions

**1.** Which of the following is INCORRECT, and not used in Archimedes proof of his theory?

**2.** What did Euclid do in his 48th proposition?

**3.** Which of the following can not be solved using algebra?

**4.** Where did Hippocrates come from?

**5.** What did most of Heron's work deal with?

This section contains 509 words(approx. 2 pages at 300 words per page) |