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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. Who was Eratosthanes?**
**(a)** He was a teacher and philosopher. **(b)** He was a mathematician, and leading doctor. **(c)** He was the chief librarian, and a mathematician. **(d)** He was the first to study political sciences.

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

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

**4. According to Euclid, when is a triangle a right triangle?**
**(a)** When a triangle has three sides whose squares are equal to the area of the triangle. **(b)** When a triangle can be constructed with three unequal sides. **(c)** When a triangle has a side whose square is the sum of the squares of the two legs. **(d)** When a triangle does not have a side which can be considered a hypotenuse.

**5. As described by Dunham, what did Archimedes demonstrate first in his proof on pi?**
**(a)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's diameter. **(b)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's diameter and the other leg equal to the circle's circumference. **(c)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's circumference. **(d)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's hypotenuse and the other leg equal to the circle's circumference.

## Short Answer Questions

**1.** Who was the first of ancient philosophers to consider why geometric properties existed?

**2.** Which is a geometric concept that humans have been aware of since the dawn of agriculture?

**3.** What did Euclid do in his 48th proposition?

**4.** What did Dunham consider as Archimedes's "masterpiece"?

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

## Short Essay Questions

**1.** Describe why Dunham infers that Euclid's Elements was an evolutionary book not so much for what it said, but in how it was presented.

**2.** Describe in two sentences Archimedes's method for determining circular area.

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

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

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

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

**7.** What did Dunham explain about the shift in learning from the West to the East?

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

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

**10.** Explain who was Hippocrates, his contribution to mathematics, and how do we know about him?

This section contains 1,061 words(approx. 4 pages at 300 words per page) |