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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. What did Euler's sum surprisingly connect?
(a) The squares of area and square roots.
(b) The circumference of a circle and right triangles.
(c) The area of squares and the area of circles.
(d) The area under a curve.
2. How did Lindeman prove his conclusion?
(a) Lindeman proved that all numbers are constructable with a compass and ruler.
(b) Lindeman proved that some numbers are not constructable with only a compass and straight-edge.
(c) Lindeman proved that some numbers are constructable without the use of a compass.
(d) Lindeman proved that square roots are irrational numbers.
3. What great theorem is presented by Dunham in this chapter?
(a) A theorem on series developed by Jakob and published by Johann Bernoulli.
(b) A theorem on infinite series published by Jakob Bernoulli.
(c) A theorem on finite series developed by Johann Bernoulli.
(d) An improvement on Leibniz's caluclus as presented by Jakob Bernoulli.
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 relationship of area to circumference is really the same as the relationship of radius to diameter.
(c) That the square of a diameter is equal to pi.
(d) That the value of pi is proportional to the area of the circle.
5. Where did Euler study at the age of 20?
(a) The Academy in St. Petersburg.
(b) University of Moscow.
Short Answer Questions
1. What were the proofs in Elements based on?
2. What was the title of Cardano's book which contained the solution to the cubic?
3. What name did Euclid give for numbers that could be divided by numbers other than themselves and one?
4. How did Euler prove if the number 4,294,967,297 was prime or composite?
5. Heron devised which of the following methods?
This section contains 361 words
(approx. 2 pages at 300 words per page)