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

Multiple Choice Questions

1. 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.

2. Who's method did Tartaglia's challenger use in the contest to solve cubic equations?
(a) Pacioli's method.
(b) del Ferro's method.
(c) Fontana's method.
(d) Cardano's method.

3. What is a "depressed cubic"?
(a) A method to solve equations with two variables.
(b) A method to simpify the x squared value in a cubic equation.
(c) A method to simplify measuring complex geometric forms.
(d) A method to logically square all the factors in a cubic equation.

4. Which of the following were an example of twin primes?
(a) 11 and 13.
(b) 2 and 6.
(c) 15 and 16.
(d) 19 and 22.

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

6. What did Heron's advances put into historical perspective for Dunham?
(a) A shift in information flow that ignored socioeconomic order.
(b) A change in political theory across the globe.
(c) A shift in learning across continents.
(d) A change in learning foundations in the ancient scholarly universities.

7. Heron devised which of the following methods?
(a) A way to apply mathematics to public health.
(b) A way to determine the area of a triangle.
(c) A way to determine the volume in a sphere.
(d) A way to solve binomial equations.

8. What provided most of the content in the book Elements?
(a) Postulates.
(b) Propositions.
(c) Notions.
(d) Hypotheses.

9. Who was Eratosthanes?
(a) He was the chief librarian, and a mathematician.
(b) He was a mathematician, and leading doctor.
(c) He was the first to study political sciences.
(d) He was a teacher and philosopher.

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

11. Why did Cardano take an oath to secrecy?
(a) It was the only way he could become a priest,
(b) It was the only way to get his book published.
(c) It was to the only way to win the contest with Fior,
(d) It was the only way to get Tartaglia's solution to cubic equations.

12. What did Gauss set out to prove?
(a) That a circle can have less than 360 degrees.
(b) That a right angle is always equal to 90 degrees.
(c) That the sum of the angles in a triangle is 180 degrees.
(d) That Euclid's postulate on straight lines was incorrect.

13. Who was del Ferro's student?
(a) Niccolo Fontana.
(b) Gerolamo Cardano.
(c) Antonio Fior.
(d) Luca Pacioli.

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

15. What did Hippocrates do that advanced mathematical methods?
(a) He built theorems based on sequencially more complex proofs.
(b) He demonstrated that geometry does not have to be based on previous knowledge.
(c) He created a new ways to disprove theories.
(d) He proved that mathematics can be applied in a unlogical order.

Short Answer Questions

1. Which was true of Euclid's number theory?

2. Who wrote a treatise that supposed that cubic equations may be impossible to solve?

3. What did Euclid state about pi in Elements?

4. What was the same about Apollonius and Erosthanes?

5. Who was Heron?

(see the answer keys)

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