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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 the same about Apollonius and Erosthanes?**
**(a)** They were both mathematicians. **(b)** They both studied the Universe. **(c)** They were both born in the same year. **(d)** They both calculated the circumference of the earth.

**2. Which shapes as described by Euclid, inspired the Greek philosopher Plato?**
**(a)** Manifolds. **(b)** Regular polyhedrons. **(c)** Spheres and cones. **(d)** Triangles.

**3. Which of the following was an important proposition given by Euclid's number theory?**
**(a)** Any perfect number is divisible by some composite number. **(b)** Any even number is divisible by 3. **(c)** Numbers from one to ten are only divisible by composite numbers. **(d)** Any composite number is divisible by some prime number.

**4. What did Hippocrates do that advanced mathematical methods?**
**(a)** He proved that mathematics can be applied in a unlogical order. **(b)** He built theorems based on sequencially more complex proofs. **(c)** He demonstrated that geometry does not have to be based on previous knowledge. **(d)** He created a new ways to disprove theories.

**5. Which is a geometric concept that humans have been aware of since the dawn of agriculture?**
**(a)** Metric system. **(b)** Area. **(c)** Gravity. **(d)** Volume.

## Short Answer Questions

**1.** Who challenged Tartaglia to a contest to solve cubic equations?

**2.** Who was Neil's Abel?

**3.** Which was true of Euclid's number theory?

**4.** That properties of specific shapes were early Egyptians aware of?

**5.** As described by Dunham, what did Archimedes demonstrate first in his proof on pi?

## Short Essay Questions

**1.** Explain what Archimedes went on to study after the circle, and what was Dunham's opinion of this work.

**2.** Describe the ancient city Alexandria and name a few of its third century geniuses.

**3.** According the Dunham, how did Euclid prove his theory on the infinitude of primes?

**4.** What did Dunham claim was Pythagoras's major contribution to geometry, and mathematical reasoning?

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

**6.** Describe what the Egyptians knew about geometry and triangles before Hippocrates.

**7.** Explain some puzzles suggested by Euclid's theories.

**8.** Explain when the knowledge of ancient scholars was rediscovered.

**9.** Describe the events that follow del Ferro's death between Fior and Tartaglia.

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

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