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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 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.

**2. What instruments did the Greeks use to square a shape?**
**(a)** A sphere and ruler. **(b)** A compass and a ruled straight-edge. **(c)** A pendulum. **(d)** A small grid.

**3. What were the proofs in Elements based on?**
**(a)** Lindeman's method. **(b)** Basic definitions. **(c)** Ancient greek geometry. **(d)** Novel notions.

**4. Which of the following is an example of a perfect number?**
**(a)** 20. **(b)** 6. **(c)** 1. **(d)** 10.

**5. 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 relationship between ratios in triangles. **(c)** He studied the relationship of sine to cosine. **(d)** He studied the volume and surface area of spheres, cones, and cylinders.

## Short Answer Questions

**1.** Which of the following best describes Archimedes as discussed by Dunham?

**2.** According to Euclid, when is a triangle a right triangle?

**3.** Numbers whose divisor add up to itself, was considered which type of number according to Euclid?

**4.** Which of the following is INCORRECT, and not used in Archimedes proof of his theory?

**5.** Which of the following is an example of a postulate that must be accepted in Elements?

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