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# Journey Through Genius: The Great Theorems of Mathematics Quiz | Four Week Quiz A

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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. How did Archimedes demonstrate his theory of pi?
(a) He demonstrated that the area of the circle is never equal to the area of the triangle.
(b) He demonstrated that the area of the circle is neither greater than nor less than the area of the triangle and therefore must be equal to it.
(c) He demonstrated that the area of the circle is always greater than the area of the triangle.
(d) He demonstrated that the area of the circle is never less than the area of the triangle.

2. How do we know about Hippocrates proofs and theorems?
(a) What is known from archived documents of his time.
(b) His books and publications.
(c) What we know is from references of later mathematicians.
(d) Mathematicians rewrote all of his proofs after his death,

3. Where was Archimedes born?
(a) Rome.
(b) Sicily.
(c) Olympia.
(d) Athens.

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

5. Which of the following best describes Archimedes as discussed by Dunham?
(a) Absent-minded genius.
(b) Mild-mannered researcher.
(c) Creative but stubborn.
(d) Loud and arrogant.

## Short Answer Questions

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

2. Which of the following was one of Euclid's great theorems?

3. Who was the author of the book Elements?

4. Which of the following is INCORRECT, and not used in Archimedes proof of his theory?

5. What did Gauss set out to prove?

(see the answer key)

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