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

**2. Which of the following is true in modern math about twin primes?**
**(a)** They are infinite. **(b)** We don't know if they are finite or infinite. **(c)** Their sum is always another prime number. **(d)** They are not considered whole numbers.

**3. Which of the following was a major part of Gauss' work in mathematics?**
**(a)** Simple proofs to demonstrate Bernoulli's series. **(b)** Proofs to show that Archimedes' number theory was wrong. **(c)** Elemental proofs related to the foundations of algebra. **(d)** Proofs on the area of a square.

**4. In general, what did Euclid's number theory describe?**
**(a)** The relationship of decimals to integers. **(b)** The nature of measuring geometry. **(c)** The relationship of fractions to decimals. **(d)** The nature of whole numbers.

**5. Which of the following is an example of a postulate that must be accepted in Elements?**
**(a)** It is possible to draw an arc with any three points. **(b)** It is possible to connect any two points with a line and make a circle. **(c)** It is possible to draw a straight line between an infinite number of points. **(d)** It is possible to draw a circle that contains no lines.

## Short Answer Questions

**1.** Where did Newton go to school before he went to Cambridge?

**2.** What did Dunham consider extraordinary about the Elements?

**3.** What name did Euclid give for numbers that could be divided by numbers other than themselves and one?

**4.** What range of values did Archimedes determine for pi?

**5.** Who was Eratosthanes?

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