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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. Which of the following is true in modern math about twin primes?**
**(a)** They are infinite. **(b)** They are not considered whole numbers. **(c)** Their sum is always another prime number. **(d)** We don't know if they are finite or infinite.

**2. How many sides did the pentadecagon have, as presented by Euclid?**
**(a)** Five. **(b)** Twenty. **(c)** Fifteen. **(d)** Ten.

**3. 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 is a challenge that continues into modern mathematics. **(c)** The measurement of pi was redetermined after Archimedes's death. **(d)** The measurement of pi should not have been so difficult for Archimedes to demonstrate.

**4. After working on pi, what did Archimedes continue with in his study of mathematics?**
**(a)** He studied the volume to surface area ratios of cubes. **(b)** He studied the volume and surface area of spheres, cones, and cylinders. **(c)** He studied the relationship between ratios in triangles. **(d)** He studied the relationship of sine to cosine.

**5. What was the bases of Hippocrates's proof ?**
**(a)** Properties of points and lines. **(b)** Properties of triangles and semicircles. **(c)** Properties of squares and cubes. **(d)** Properties of area to volume measurements.

## Short Answer Questions

**1.** What did Dunham claim about Archimedes's determination of a number value for pi?

**2.** What did Dunham consider as Archimedes's "masterpiece"?

**3.** What did Archimedes manage to prove using Euclid's ideas?

**4.** How did Lindeman prove his conclusion?

**5.** In general, what did Euclid's number theory describe?

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