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

2. What is true about prime numbers?
(a) Prime numbers are not divisible by other numbers.
(b) Prime numbers can not exist in a finite series.
(c) Prime numbers can never be an odd number.
(d) That for every group of prime numbers, there exists at least one more prime.

3. What was true when Euler used n = 5 in the statement 2²ⁿ + 1?
(a) The statement was a perfect number.
(b) The statement was not a prime number.
(c) The statement was a composite number.
(d) The statement was a prime number.

4. What was true about Heron's theorem as described by Dunham?
(a) It was to determine the volume of a sphere without measuring the circumference.
(b) It was to solve equations were only two varibles are known.
(c) It was to determine the area of a circle by measuring a right triangle inside the circle.
(d) It was to find the area of a triangle when only the length of the sides are known.

5. Which of Euclid's postulates troubled many of the following generations of mathematicians?
(a) Euclid's postulate on right triangles.
(b) Euclid's postulate on parallel lines.
(c) Euclid's postulate on creating an arc.
(d) Euclid's proof on right triangles.

Short Answer Questions

1. Which of the following was NOT one of the basic definitions in Elements?

2. Which of the following demonstrates the successive squared denominator series?

3. Where was the modern number system developed?

4. What did Euler's sum surprisingly connect?

5. Which of the following is an example of a perfect number?

(see the answer key)

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