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This test consists of 15 multiple choice questions and 5 short answer questions.

Multiple Choice Questions

1. What allowed Cardano to justify publishing his book?
(a) He was punished as a heretic,
(b) He found del Ferro's orgininal solution to the cubic.
(c) He was dead, and the book was really published by his student.
(d) He found Fior's documents which spoke against Tartaglia.

2. Who challenged Tartaglia to a contest to solve cubic equations?
(a) del Ferro.
(b) Pacioli.
(c) Cardano.
(d) Fior.

3. What did Dunham discuss for many pages in this chapter?
(a) Heron's origins of the universe.
(b) Heron's religious beliefs-
(c) Heron's complicated proof.
(d) Heron's political tendancy.

4. What was Eratosthanes most famous for?
(a) He developed a simple way to find prime numbers and for determining the circumference of the Earth.
(b) He showed that there are no even prime numbers.
(c) He showed that the Earth must be a sphere.
(d) He developed a way to navigate using logitude and latitude.

5. Which of the following is an example of a postulate that must be accepted in Elements?
(a) It is possible to connect any two points with a line and make a circle.
(b) It is possible to draw an arc with any three points.
(c) It is possible to draw a straight line between an infinite number of points.
(d) It is possible to draw a circle that contains no lines.

6. What do we know in modern times about Heron?
(a) We know he was a teacher and philosopher but much of his work has been lost.
(b) We know he was an influencial scholar, but we don't know who his students were.
(c) We know he lived in Rome.
(d) We know very little, but much of his work survives.

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

8. What was known about pi, during Archimedes' time?
(a) That it could not be assigned a relationship between measurements in a circle.
(b) That is was the relationship between the diameter and circumference of a circle.
(c) Nothing, the concept of pi was unknown.
(d) That it was never the same number value for a given circle.

9. When was the work of these early thinkers rediscovered again in history?
(a) In the 20th century.
(b) In the Renaissance.
(c) In the 18th century.
(d) In the Elizabethian age.

10. Which of the following is true in modern math about twin primes?
(a) They are infinite.
(b) They are not considered whole numbers.
(c) We don't know if they are finite or infinite.
(d) Their sum is always another prime number.

11. 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 hypotenuse and the other leg equal to the circle's circumference.
(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 radius and the other leg equal to the circle's diameter.

12. Which was true of Euclid's number theory?
(a) It has an impact on modern math.
(b) It was incorrect, as proved by Plato.
(c) It has been proven too basic to be useful.
(d) It was proven to the true by Hippocrates.

13. What was the bases of Hippocrates's proof ?
(a) Properties of triangles and semicircles.
(b) Properties of squares and cubes.
(c) Properties of points and lines.
(d) Properties of area to volume measurements.

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

15. What did Dunham claim about Archimedes's determination of a number value for pi?
(a) Archimedes's number could have been better if he had understood Euclid's work better,
(b) Archimedes's number was very good, considering he did not have a way to calculate square roots.
(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. Which of the following best describes Archimedes as discussed by Dunham?

2. What else, besides a solution to cubic equations, was in Cardano's book?

3. Where was Archimedes born?

4. What instruments did the Greeks use to square a shape?

5. That properties of specific shapes were early Egyptians aware of?

(see the answer keys)

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