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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?

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