|Name: _________________________||Period: ___________________|
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?
(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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