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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 was the title of Cardano's book which contained the solution to the cubic?**
**(a)** La Magnifica. **(b)** Tarsisia. **(c)** Ars Magna. **(d)** Elements.

**2. Which of the following could NOT be included as a step in Euclid's great theorem?**
**(a)** Divide a infinite group of primes by the sum of their composites. **(b)** If a new number is found to be composite, then it must have some prime as a divisor. **(c)** After summation, the new number can be prime or composite. **(d)** Take a finite group of primes and add them together, plus one.

**3. What was Euclid's definition of a prime number?**
**(a)** Numbers which are divisible by 2. **(b)** Numbers which do not, and can not, contain a perfect number. **(c)** Numbers which contain an infinite number of composite numbers. **(d)** Numbers which can only be divided by themselves and 1.

**4. How did Archimedes arrive at a number value for pi?**
**(a)** By proving pi could not be equal to one. **(b)** By constructing multi-sided polygons inside and outside a circle and determining their perimeters. **(c)** By proving that pi could not be a negative number. **(d)** By constructing successively smaller circles inside circles until he realized all of their ratios of diameter to area were equal.

**5. Who was Eratosthanes?**
**(a)** He was the first to study political sciences. **(b)** He was a mathematician, and leading doctor. **(c)** He was the chief librarian, and a mathematician. **(d)** He was a teacher and philosopher.

## Short Answer Questions

**1.** In his later life, what position did Isaac Newton hold?

**2.** In Elements, how many postulates must be accepted as given?

**3.** Dunham showed that Heron's proof could also be used as which of the following?

**4.** Which of the following was a major part of Gauss' work in mathematics?

**5.** What was similar about both Euler and Gauss as children?

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