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This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.

## Multiple Choice Questions

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

**2. What do we know in modern times about Heron?**
**(a)** We know very little, but much of his work survives. **(b)** We know he lived in Rome. **(c)** We know he was an influencial scholar, but we don't know who his students were. **(d)** We know he was a teacher and philosopher but much of his work has been lost.

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

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

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

## Short Answer Questions

**1.** Which of the following could NOT be included as a step in Euclid's great theorem?

**2.** What did Plato use his inspiration from Euclid for?

**3.** What was Euclid's definition of a prime number?

**4.** Which was true of Euclid's number theory?

**5.** What did Heron's advances put into historical perspective for Dunham?

## Short Essay Questions

**1.** Explain why Archimedes finding a number value for pi was considered a great achievement according to Dunham.

**2.** Describe how Cardano eventually publishes the solution to cubic equations.

**3.** Describe what mathematical and artistic movements are focused on in the second half of the 19th century.

**4.** What did Dunham describe in the epilogue of the chapter?

**5.** Explain any methods used by Cantor that were unsuccessful.

**6.** How did Archimedes find a number value for pi?

**7.** Describe the connection between Fermat and Euler's work.

**8.** Why did Euler start working on the sum of series?

**9.** Describe some of the characteristics of Leonhard Euler, and what made him successful.

**10.** What were the two transfinite cardinals discovered by Cantor, and what method did he use to determine them?

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