STRAIGHT-LINE AND COMPASS CONSTRUCTIONS.

Problem 9

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

9. Show how you can construct a line segment 1/2 inch long, 1/4, 1/8, etc.

Solution

1. Draw a line segment of 1 inch. Let its endpoints be a and b.
2. Find the midpoint of ab. This is 1/2 inch from a.
3. Call this point c.
4. By repeated bisections of smaller and smaller line segments, the required lengths can be constructed.