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This quiz consists of 5 multiple choice and 5 short answer questions through The Bernoullis and the Harmonic Series.

## Multiple Choice Questions

**1. What is the name for determining the area of an enclosed space by constructing a square of equivalent area?**
**(a)** Square root. **(b)** Triangulation. **(c)** Quadrature. **(d)** Cubation.

**2. Which of the following could NOT be included as a step in Euclid's great theorem?**
**(a)** After summation, the new number can be prime or composite. **(b)** Divide a infinite group of primes by the sum of their composites. **(c)** Take a finite group of primes and add them together, plus one. **(d)** If a new number is found to be composite, then it must have some prime as a divisor.

**3. According to Dunham, who was most able to collect knowledge from around the globe?**
**(a)** Greek philosophers. **(b)** Roman emporers. **(c)** Greek tradesman. **(d)** Arabian scholars.

**4. Who wrote a treatise that supposed that cubic equations may be impossible to solve?**
**(a)** Scipione del Ferro. **(b)** Niccolo Fontana. **(c)** Luca Pacioli. **(d)** Gerolamo Cardano.

**5. In general, what did Euclid's number theory describe?**
**(a)** The nature of whole numbers. **(b)** The nature of measuring geometry. **(c)** The relationship of fractions to decimals. **(d)** The relationship of decimals to integers.

## Short Answer Questions

**1.** Which city was the center of thinking and learning in Third century BC?

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

**3.** In what century did Archimedes live?

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

**5.** Who was the first of ancient philosophers to consider why geometric properties existed?

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