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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. Where did Newton go to school before he went to Cambridge?**
**(a)** Cambridge Prep. **(b)** Charles II Grammar School. **(c)** The King's School. **(d)** Oxford Grammar School.

**2. Which of the following demonstrates the successive squared denominator series?**
**(a)** 1 + 1/2 + 1/6 + 1/10 + 1/15 . . . **(b)** 1 + 1/4 + 1/9 + 1/16 . . . **(c)** 1 + 1/2 + 1/3 + 1/4 + 1/5 . . . 1/1000 . . . **(d)** 1 + 1/2 + 3/4 + 4/5 . . .

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

**4. What name did Euclid give for numbers that could be divided by numbers other than themselves and one?**
**(a)** Even numbers. **(b)** Perfect numbers. **(c)** Composite numbers. **(d)** Discrete numbers.

**5. As described by Dunham, what did Archimedes demonstrate first in his proof on pi?**
**(a)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's hypotenuse and the other leg equal to the circle's circumference. **(b)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's diameter and the other leg equal to the circle's circumference. **(c)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's diameter. **(d)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's circumference.

## Short Answer Questions

**1.** In what area was Gauss especially interested?

**2.** What did Euler prove about 2²ⁿ + 1?

**3.** Where was Archimedes born?

**4.** What is true about prime numbers?

**5.** What is one proof that Euler was able to prove?

This section contains 372 words(approx. 2 pages at 300 words per page) |