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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. Which of the following could NOT be included as a step in Euclid's great theorem?
(a) Divide a infinite group of primes by the sum of their composites.
(b) Take a finite group of primes and add them together, plus one.
(c) If a new number is found to be composite, then it must have some prime as a divisor.
(d) After summation, the new number can be prime or composite.

2. Exactly what limit is reached at a quartic equation?
(a) The limit of algebra.
(b) The limit of the Pythagorean Theorem.
(c) The limit of logical geometric proofs.
(d) The limit of the decompressed cubic method.

3. Which of the following becomes an important definition in mathematics that was first presented in Elements?
(a) Parallel line.
(b) Intersection.
(c) Circle.
(d) 180 degree angle.

4. Which of Euclid's postulates troubled many of the following generations of mathematicians?
(a) Euclid's postulate on creating an arc.
(b) Euclid's proof on right triangles.
(c) Euclid's postulate on parallel lines.
(d) Euclid's postulate on right triangles.

5. What was true about Hippocrates's proof?
(a) The proof was easy if their was advanced technology available.
(b) It was useful for circles.
(c) It was fairly easy and simple.
(d) The proof was exceedingly difficult and not understood at the time.

Short Answer Questions

1. How did Archimedes demonstrate his theory of pi?

2. Which of the following best describes Archimedes as discussed by Dunham?

3. How did Archimedes arrive at a number value for pi?

4. Who was del Ferro's student?

5. What did Euclid state about pi in Elements?

Short Essay Questions

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

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

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

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

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

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

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

8. What was already known about circles before Archimedes?

9. 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.

10. Explain who was Gerolamo Cardano, and how did he become involved with the solution to the cubic.

(see the answer keys)

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