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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 range of values did Archimedes determine for pi?**
**(a)** Between 3 10/11 and 3 1/7. **(b)** Between 3 and 4. **(c)** Between 3 1/2 and 3 5/8. **(d)** Between 3 and 3 1/2.

**2. On who's work did Euler base his number theory?**
**(a)** Bernoulli's. **(b)** Fermat's. **(c)** Newton's. **(d)** Leibniz's.

**3. What did Apollonius work with in mathematics?**
**(a)** He worked on conics. **(b)** He worked on advanced algebra. **(c)** He develped a way to measure the volume of a sphere. **(d)** He discovered the algrebraic equation.

**4. Dunham showed that Heron's proof could also be used as which of the following?**
**(a)** A proof of Hippocrates' squared areas. **(b)** A proof of Euclid's number theory **(c)** A proof of the Pythagorean Theorem. **(d)** A proof of Archimedes' number theory.

**5. What does the Pythagorean Theorem state?**
**(a)** For any triangle the sum of the legs squared is equal to the length of the hypotenuse. **(b)** For any right triangle the diagonal side is equal to the sum of the legs. **(c)** For any right triangle the square of the diagonal side is equal to the sum of the squares of the two legs. **(d)** For any triangle the sqaured sum of the legs is equal to half the hypotenuse.

## Short Answer Questions

**1.** Which mathematician was first to take the challenge to solve cubic equations?

**2.** What was the same about the series proposed by Leibniz and the series proposed by Bernoulli?

**3.** What else, besides a solution to cubic equations, was in Cardano's book?

**4.** Which name does NOT belong?

**5.** What was true when Euler used n = 5 in the statement 2²ⁿ + 1?

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