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This quiz consists of 5 multiple choice and 5 short answer questions through Heron's Formula for Triangular Area.

## Multiple Choice Questions

**1. What was known about pi, during Archimedes' time?**
**(a)** That is was the relationship between the diameter and circumference of a circle. **(b)** Nothing, the concept of pi was unknown. **(c)** That it was never the same number value for a given circle. **(d)** That it could not be assigned a relationship between measurements in a circle.

**2. 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.

**3. What did Heron's advances put into historical perspective for Dunham?**
**(a)** A shift in learning across continents. **(b)** A change in political theory across the globe. **(c)** A shift in information flow that ignored socioeconomic order. **(d)** A change in learning foundations in the ancient scholarly universities.

**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 of sine to cosine. **(d)** He studied the relationship between ratios in triangles.

**5. What did Dunham claim about Archimedes's determination of a number value for pi?**
**(a)** Archimedes's number was perfectly correct. **(b)** Archimedes's number could have been better if he had understood Euclid's work better, **(c)** Archimedes's number was not very accurate, considering the technology of his time. **(d)** Archimedes's number was very good, considering he did not have a way to calculate square roots.

## Short Answer Questions

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

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

**3.** Which of the following was NOT defined by Euclid?

**4.** What did Dunham consider extraordinary about the Elements?

**5.** What did Ferdinand Lindeman prove in 1882?

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