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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 Heron?
(a) A politician from Rome.
(b) A philosopher from Greece.
(c) A matematician from Alexanderia.
(d) A physician from the far East.

2. Who was the first of ancient philosophers to consider why geometric properties existed?
(a) Hippocrates.
(b) Aristotle.
(c) Pythagoras.
(d) Thales.

3. What did Apollonius work with in mathematics?
(a) He discovered the algrebraic equation.
(b) He worked on conics.
(c) He develped a way to measure the volume of a sphere.
(d) He worked on advanced algebra.

4. What was most useful about finding the square of a shape, before Hippocrates?
(a) It was useful in finding the area of oddly shaped pieces of land.
(b) It was useful in creating simple elevation maps,
(c) It was useful in finding the area of circles.
(d) It was useful in determining the distance between two points.

5. 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) Any composite number is divisible by some prime number.
(d) Numbers from one to ten are only divisible by composite numbers.

Short Answer Questions

1. Which of the following was one of Euclid's great theorems?

2. According to Euclid, when is a triangle a right triangle?

3. Which city was the center of thinking and learning in Third century BC?

4. What name did Euclid give for numbers that could be divided by numbers other than themselves and one?

5. What did Heron's advances put into historical perspective for Dunham?

Short Essay Questions

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

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

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

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

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

6. 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.

7. Describe Euclid's definition of prime numbers and the relationship he stated as existing between prime and composite numbers.

8. Describe what Gauss discovered according to Dunham.

9. Describe the contents of Cardano's book.

10. Explain when the knowledge of ancient scholars was rediscovered.

(see the answer keys)

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