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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. That properties of specific shapes were early Egyptians aware of?
(a) Parallelograms.
(b) Pi and the diameter of a circle.
(c) Right triangles.
(d) Irregular solids.

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

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

4. What range of values did Archimedes determine for pi?
(a) Between 3 10/11 and 3 1/7.
(b) Between 3 1/2 and 3 5/8.
(c) Between 3 and 3 1/2.
(d) Between 3 and 4.

5. How did Lindeman prove his conclusion?
(a) Lindeman proved that all numbers are constructable with a compass and ruler.
(b) Lindeman proved that some numbers are constructable without the use of a compass.
(c) Lindeman proved that square roots are irrational numbers.
(d) Lindeman proved that some numbers are not constructable with only a compass and straight-edge.

Short Answer Questions

1. Which of the following is false about the modern implications of Euclid's number theory?

2. Which shapes as described by Euclid, inspired the Greek philosopher Plato?

3. Who challenged Tartaglia to a contest to solve cubic equations?

4. Which of the following becomes an important definition in mathematics that was first presented in Elements?

5. Which is one of the common notions presented in Elements?

(see the answer key)

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