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

2. After working on pi, what did Archimedes continue with in his study of mathematics?
(a) He studied the volume and surface area of spheres, cones, and cylinders.
(b) He studied the volume to surface area ratios of cubes.
(c) He studied the relationship of sine to cosine.
(d) He studied the relationship between ratios in triangles.

3. What was Euclid's definition of a prime number?
(a) Numbers which contain an infinite number of composite numbers.
(b) Numbers which are divisible by 2.
(c) Numbers which can only be divided by themselves and 1.
(d) Numbers which do not, and can not, contain a perfect number.

4. What did Archimedes manage to prove using Euclid's ideas?
(a) That the area of a circle and the square of its diameter is really the same as the relationship of diameter to circumference.
(b) That the square of a diameter is equal to pi.
(c) That the value of pi is proportional to the area of the circle.
(d) That the relationship of area to circumference is really the same as the relationship of radius to diameter.

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

Short Answer Questions

1. What did Heron's advances put into historical perspective for Dunham?

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

3. Besides being a mathematician, what else other work was Archimedes famous for?

4. Which of the following was an important proposition given by Euclid's number theory?

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

(see the answer key)

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