1. How did Archimedes demonstrate his theory of pi?
(a) He demonstrated that the area of the circle is never less than the area of the triangle.
(b) 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.
(c) He demonstrated that the area of the circle is always greater than the area of the triangle.
(d) He demonstrated that the area of the circle is never equal to the area of the triangle.

2. What did Dunham consider as Archimedes's "masterpiece"?
(a) Archimedes' work on volume to surface area ratios.
(b) Archimedes' work on determining angular measurements.
(c) Archimedes' work on shperes, cones, and cylinders.
(d) Archimedes' work on determining a number value for pi.

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

4. Who was the first of ancient philosophers to consider why geometric properties existed?
(a) Thales.
(b) Pythagoras.
(c) Aristotle.
(d) Hippocrates.

5. How did Archimedes arrive at a number value for pi?
(a) By constructing successively smaller circles inside circles until he realized all of their ratios of diameter to area were equal.
(b) By proving that pi could not be a negative number.
(c) By constructing multi-sided polygons inside and outside a circle and determining their perimeters.
(d) By proving pi could not be equal to one.