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This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.

## Multiple Choice Questions

**1. What was Euclid's definition of a prime number?**
**(a)** Numbers which can only be divided by themselves and 1. **(b)** Numbers which contain an infinite number of composite numbers. **(c)** Numbers which are divisible by 2. **(d)** Numbers which do not, and can not, contain a perfect number.

**2. Who wrote a treatise that supposed that cubic equations may be impossible to solve?**
**(a)** Niccolo Fontana. **(b)** Gerolamo Cardano. **(c)** Luca Pacioli. **(d)** Scipione del Ferro.

**3. What did Plato use his inspiration from Euclid for?**
**(a)** To construct his theory on the shape of the Universe. **(b)** To prove Euclid's number theory was incorrect. **(c)** To create a new theorem of algebra. **(d)** To classify geometric shapes by their complexity.

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

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

## Short Answer Questions

**1.** What did Gauss set out to prove?

**2.** What was Hippocrates famous for?

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

**4.** In what century did Archimedes live?

**5.** Who acted as the gate keepers of knowledge?

## Short Essay Questions

**1.** What was the great theorem of this chapter? Describe it briefly.

**2.** Who was Luca Pacioli, and what controversy was sparked over his writings?

**3.** Who was Heron, and what is known about him today?

**4.** Explain in two sentences Euclid's method to prove the Pythagorean Theorem.

**5.** Describe what work of Euclid's fascinated Plato and his theory on the shape of the Universe.

**6.** Explain how Gottfried Leibniz was able to publish his method of calculus.

**7.** Summarize, in a sentence, what was Hippocates's great theorem, and what was it based on according to Dunham?

**8.** What was Euler able to prove about 2²ⁿ + 1? Why was this a great accomplishment?

**9.** What did Euclid state for his theory on prime numbers?

**10.** Explain why Eulers sum of Ï€Â²/6 was in some ways surprising.

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