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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 shape was NOT demonstrated in the Elements as having a relationship to other shapes?
(a) Hyperbola.
(b) Pentagon.
(c) Triangle.
(d) Hexagon.

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

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

4. Which of the following is true about pi, as described by Dunham.
(a) The measurement of pi is no longer a mystery as we have an exact number value in modern mathematics.
(b) The measurement of pi should not have been so difficult for Archimedes to demonstrate.
(c) The measurement of pi was redetermined after Archimedes's death.
(d) The measurement of pi is a challenge that continues into modern mathematics.

5. Which is a geometric concept that humans have been aware of since the dawn of agriculture?
(a) Gravity.
(b) Volume.
(c) Area.
(d) Metric system.

Short Answer Questions

1. Which of the following was NOT one of the basic definitions in Elements?

2. What provided most of the content in the book Elements?

3. Exactly what limit is reached at a quartic equation?

4. What was known about pi, during Archimedes' time?

5. In what time period did mathematicians find a solution to cubic equations?

Short Essay Questions

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

2. How many definitions were in Euclid's book? List some of the definitions he included.

3. Explain in two sentences Euclid's method to prove the Pythagorean Theorem.

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

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

6. What was already known about circles before Archimedes?

7. Describe what is quadrature and why it was useful in the time of Hippocrates.

8. What was Euclid's definition of composite and perfect numbers?

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

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

(see the answer keys)

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