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This quiz consists of 5 multiple choice and 5 short answer questions through A Sampler of Euler's Number Theory.

Multiple Choice Questions

1. 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 creating simple elevation maps,
(c) It was useful in finding the area of oddly shaped pieces of land.
(d) It was useful in finding the area of circles.

2. How did Archimedes demonstrate his theory of pi?
(a) He demonstrated that the area of the circle is neither greater than nor less than the area of the triangle and therefore must be equal to it.
(b) He demonstrated that the area of the circle is always greater than the area of the triangle.
(c) He demonstrated that the area of the circle is never less than the area of the triangle.
(d) He demonstrated that the area of the circle is never equal to the area of the triangle.

3. Which of the following is a series that the Bernoullis proposed did not converge on a finite sum?
(a) 1 + 1/2 + 1/3 + 1/4 + 1/5 . . . 1/1000 . . .
(b) 1 + 1/2 + 1/6 + 1/10 + 1/15 . . .
(c) 1 + 2 + 3 + 4 + 5. . .
(d) 1 + 1/2 + 3/4 + 4/5 . . .

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

5. What else, besides a solution to cubic equations, was in Cardano's book?
(a) An alegrabic solution to quintic equations,
(b) A suggested method to depress all complex geometry.
(c) A proof of the Pythagorean Theorem.
(d) A solution to quartic equations.

Short Answer Questions

1. Who acted as the gate keepers of knowledge?

2. What did Archimedes manage to prove using Euclid's ideas?

3. Who was del Ferro's student?

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

5. Heron's work referred to the work of what other famous scholar?

(see the answer key)

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