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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 could NOT be included as a step in Euclid's great theorem?**
**(a)** After summation, the new number can be prime or composite. **(b)** Take a finite group of primes and add them together, plus one. **(c)** Divide a infinite group of primes by the sum of their composites. **(d)** If a new number is found to be composite, then it must have some prime as a divisor.

**2. "Straight lines in the same plane that will never meet if extended forever" is a definition of what?**
**(a)** Circle. **(b)** Parallel lines. **(c)** 180 degree angle. **(d)** Intersection.

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

**4. How many definitions were stated in Elements?**
**(a)** Five. **(b)** Twenty-three. **(c)** Thirty. **(d)** Eighteen.

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

## Short Answer Questions

**1.** What was Hippocrates's great advance to mathematics?

**2.** What was the bases of Hippocrates's proof ?

**3.** Which of the following is true about pi, as described by Dunham.

**4.** Which of the following were an example of twin primes?

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

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