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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)