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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 was true about Hippocrates's proof?**
**(a)** It was fairly easy and simple. **(b)** The proof was easy if their was advanced technology available. **(c)** The proof was exceedingly difficult and not understood at the time. **(d)** It was useful for circles.

**2. What was Hippocrates's great advance to mathematics?**
**(a)** He showed how to simplify the area of a triangle. **(b)** He showed how to square a circle. **(c)** He showed how to find the angles in a right triangle. **(d)** He showed how to square a figure with curved sides.

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

**4. How did Archimedes demonstrate his theory of pi?**
**(a)** He demonstrated that the area of the circle is always greater than 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 never less than the area of the triangle. **(d)** He demonstrated that the area of the circle is never equal to the area of the triangle.

**5. Which of the following was NOT one of the basic definitions in Elements?**
**(a)** Right angles. **(b)** Parabola. **(c)** Line. **(d)** Straight Line.

## Short Answer Questions

**1.** Which of the following was an important proposition given by Euclid's number theory?

**2.** What provided most of the content in the book Elements?

**3.** What name did Euclid give for numbers that could be divided by numbers other than themselves and one?

**4.** How many definitions were stated in Elements?

**5.** After working on pi, what did Archimedes continue with in his study of mathematics?

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