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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 Euclid state about pi in Elements?
(a) There is a constant relationship between the area of a circle and the square of its diameter.
(b) The proportion of area to circumference is never equal.
(c) The proportion of diameter to area is never equal.
(d) There is no relationship between the area of a circle and its circumference.

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 constructable without the use of a compass.
(c) Lindeman proved that square roots are irrational numbers.
(d) Lindeman proved that some numbers are not constructable with only a compass and straight-edge.

3. Which of the following was one of Euclid's great theorems?
(a) Prime numbers are more comples than discrete numbers.
(b) There exists only infinite and whole numbers.
(c) There exists an infinite number of prime numbers.
(d) There exists an finite number of prime numbers.

4. How did Gauss feel about his best work?
(a) He was uncertain if it was useful.
(b) He was unceratin if it would be accepted by his collegues.
(c) He was confident that his students would find it of great importance.
(d) He was confident that it would change mathematics.

5. What did Ferdinand Lindeman prove in 1882?
(a) It is possible to find the square of a circle.
(b) That the square root of the hypotenuse of a right triangle can not be found.
(c) That the square of a circle can not be found with a compass and a straight-edge.
(d) It is impossible to find the square of a semicircle.

Short Answer Questions

1. Where does the center of mathematical thinking shift to after Italy?

2. "Straight lines in the same plane that will never meet if extended forever" is a definition of what?

3. Which of Euclid's postulates troubled many of the following generations of mathematicians?

4. What was most useful about finding the square of a shape, before Hippocrates?

5. What did Euler prove about 2²ⁿ + 1?

(see the answer key)

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