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This quiz consists of 5 multiple choice and 5 short answer questions through Cardano and the Solution of the Cubic.

Multiple Choice Questions

1. What does the Pythagorean Theorem state?
(a) For any right triangle the diagonal side is equal to the sum of the legs.
(b) For any right triangle the square of the diagonal side is equal to the sum of the squares of the two legs.
(c) For any triangle the sum of the legs squared is equal to the length of the hypotenuse.
(d) For any triangle the sqaured sum of the legs is equal to half the hypotenuse.

2. 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 perfectly correct.
(c) Archimedes's number was not very accurate, considering the technology of his time.
(d) Archimedes's number was very good, considering he did not have a way to calculate square roots.

3. Which of the following is an example of a perfect number?
(a) 6.
(b) 20.
(c) 1.
(d) 10.

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

5. Which shapes as described by Euclid, inspired the Greek philosopher Plato?
(a) Triangles.
(b) Regular polyhedrons.
(c) Spheres and cones.
(d) Manifolds.

Short Answer Questions

1. As described by Archimedes, what is always true about he diameter of the circle?

2. Which of the following was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?

3. How many definitions were stated in Elements?

4. What is a "depressed cubic"?

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

(see the answer key)

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