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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. **(c)** Cambrigde. **(d)** Oxford.

## 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?

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