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This quiz consists of 5 multiple choice and 5 short answer questions through Archimedes' Determination of Circular Area.

Multiple Choice Questions

1. According to Euclid, when is a triangle a right triangle?
(a) When a triangle has three sides whose squares are equal to the area of the triangle.
(b) When a triangle can be constructed with three unequal sides.
(c) When a triangle has a side whose square is the sum of the squares of the two legs.
(d) When a triangle does not have a side which can be considered a hypotenuse.

2. In general, what did Euclid's number theory describe?
(a) The nature of whole numbers.
(b) The nature of measuring geometry.
(c) The relationship of fractions to decimals.
(d) The relationship of decimals to integers.

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

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

5. As described by Archimedes, what is always true about he diameter of the circle?
(a) It's equal to pi.
(b) It's always proportional to its circumference.
(c) It's never proportional to its circumference.
(d) It's equal to the square of the radius.

Short Answer Questions

1. What was true about Hippocrates's proof?

2. What was most useful about finding the square of a shape, before Hippocrates?

3. What instruments did the Greeks use to square a shape?

4. Which of the following were an example of twin primes?

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

(see the answer key)

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