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This quiz consists of 5 multiple choice and 5 short answer questions through Archimedes' Determination of Circular Area.

Multiple Choice Questions

1. What did the Pythagorean Theorem accomplish for mathematics?
(a) The concept of constructing useful mathematics.
(b) The ability to find square roots.
(c) The concept of providing a logical proof.
(d) The ability to measure angles.

2. Which of the following is false about the modern implications of Euclid's number theory?
(a) Great mathematicians continue to puzzle over some aspects of Euclid's number theory.
(b) Whether there are no odd perfect numbers is still not known.
(c) Euclid gave a good idea for how to construct even perfect numbers.
(d) Euclid's recipe for constructing even perfect numbers is incorrect.

3. What was Hippocrates famous for?
(a) His theorem on the quadrature of the lune.
(b) His proof on right triangles.
(c) His proof defining gravity.
(d) His ability to construct circles without a compass.

4. In Elements, how many postulates must be accepted as given?
(a) Eighteen.
(b) Twelve,
(c) Five.
(d) Twenty-two.

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

Short Answer Questions

1. Which of the following could NOT be included as a step in Euclid's great theorem?

2. What is the name for determining the area of an enclosed space by constructing a square of equivalent area?

3. What was true about Hippocrates's proof?

4. Which of the following is an example of a postulate that must be accepted in Elements?

5. Which of the following best describes Archimedes as discussed by Dunham?

(see the answer key)

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