STRAIGHT-LINE AND COMPASS CONSTRUCTIONS.

Problem 8

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

8. Show how you can construct a line segment 2 inches long, 3, 4, 5, 6, and so on.

Solution

1. Draw a line, A.
2. Mark an arbitrary starting point on A; call this a0.
3. Set the compasses to the length of the given 1-inch line segment.
4. Centred on a, draw a circle of radius one inch. Let one of the intersections of this circle with A be a1.
5. The line segment a0a1 is of length 1 inch.
6. Construct a circle, radius 1 inch, centred on a1.
7. Let the point of intersection of this circle and A not already labelled be a2.
8. The line segment a0a2 is of length 2 inches.
9. Repeat this construction to make line segments of arbitrary positive-integer multiples of 1 inch in length.