STRAIGHT-LINE AND COMPASS CONSTRUCTIONS.

Problem 14

Suppose you're shown a line segment and told that it is (exactly) one inch long.

14. Show how you can construct a line of length m/n, for any integers m and n.

Solution

1. We can construct lines of length m and n.
2. As a consequence of the previous two solutions, we can construct a line of length x times (1/y) or x/y, given x and y.
3. This result follows simply.