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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. 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.
2. What did the Pythagorean Theorem accomplish for mathematics?
(a) The ability to find square roots.
(b) The ability to measure angles.
(c) The concept of constructing useful mathematics.
(d) The concept of providing a logical proof.
3. Where was the modern number system developed?
(a) In ancient Rome.
(b) In ancient Alexanderia.
(c) In the West.
(d) In the East.
4. What did Archimedes manage to prove using Euclid's ideas?
(a) That the area of a circle and the square of its diameter is really the same as the relationship of diameter to circumference.
(b) That the square of a diameter is equal to pi.
(c) That the value of pi is proportional to the area of the circle.
(d) That the relationship of area to circumference is really the same as the relationship of radius to diameter.
5. What is a "depressed cubic"?
(a) A method to solve equations with two variables.
(b) A method to logically square all the factors in a cubic equation.
(c) A method to simplify measuring complex geometric forms.
(d) A method to simpify the x squared value in a cubic equation.
Short Answer Questions
1. Dunham showed that Heron's proof could also be used as which of the following?
2. What was the title of Cardano's book which contained the solution to the cubic?
3. Who's method did Tartaglia's challenger use in the contest to solve cubic equations?
4. In general, what did Euclid's number theory describe?
5. What did Dunham consider extraordinary about the Elements?
This section contains 369 words
(approx. 2 pages at 300 words per page)