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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 name did Euclid give for numbers that could be divided by numbers other than themselves and one?
(a) Composite numbers.
(b) Discrete numbers.
(c) Even numbers.
(d) Perfect numbers.

2. How did Archimedes arrive at a number value for pi?
(a) By proving that pi could not be a negative number.
(b) By constructing successively smaller circles inside circles until he realized all of their ratios of diameter to area were equal.
(c) By constructing multi-sided polygons inside and outside a circle and determining their perimeters.
(d) By proving pi could not be equal to one.

3. What instruments did the Greeks use to square a shape?
(a) A pendulum.
(b) A sphere and ruler.
(c) A compass and a ruled straight-edge.
(d) A small grid.

4. Where was the modern number system developed?
(a) In ancient Rome.
(b) In the West.
(c) In the East.
(d) In ancient Alexanderia.

5. What did Dunham claim about Archimedes's determination of a number value for pi?
(a) Archimedes's number was very good, considering he did not have a way to calculate square roots.
(b) Archimedes's number could have been better if he had understood Euclid's work better,
(c) Archimedes's number was perfectly correct.
(d) Archimedes's number was not very accurate, considering the technology of his time.

Short Answer Questions

1. Where was Neil's Abel from?

2. Who's method did Tartaglia's challenger use in the contest to solve cubic equations?

3. Which words best describe how solid proofs were developed in Elements?

4. In what century did Archimedes live?

5. What did the Pythagorean Theorem accomplish for mathematics?

Short Essay Questions

1. How did Heron find the area of a triangle, and what did Dunham state about Heron's work?

2. What was already known about circles before Archimedes?

3. Explain what Neils Abel proved.

4. Why did Euclid's postulate on parallel lines trouble mathematicians for centuries?

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

6. Describe how Cardano eventually publishes the solution to cubic equations.

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

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

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

10. 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.

(see the answer keys)

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