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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 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.

**2. Which of the following is true about pi, as described by Dunham.**
**(a)** The measurement of pi is no longer a mystery as we have an exact number value in modern mathematics. **(b)** The measurement of pi should not have been so difficult for Archimedes to demonstrate. **(c)** The measurement of pi is a challenge that continues into modern mathematics. **(d)** The measurement of pi was redetermined after Archimedes's death.

**3. How did Lindeman prove his conclusion?**
**(a)** Lindeman proved that some numbers are not constructable with only a compass and straight-edge. **(b)** Lindeman proved that some numbers are constructable without the use of a compass. **(c)** Lindeman proved that all numbers are constructable with a compass and ruler. **(d)** Lindeman proved that square roots are irrational numbers.

**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. That properties of specific shapes were early Egyptians aware of?**
**(a)** Pi and the diameter of a circle. **(b)** Parallelograms. **(c)** Irregular solids. **(d)** Right triangles.

## Short Answer Questions

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

**2.** How many sides did the pentadecagon have, as presented by Euclid?

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

**4.** Which of Euclid's postulates troubled many of the following generations of mathematicians?

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

This section contains 398 words(approx. 2 pages at 300 words per page) |