STRAIGHT-LINE AND COMPASS CONSTRUCTIONS.

Problem 15

15. Construct a regular 12-sided polygon.

Solution

1. Pick an arbitrary point, a.
2. Draw a circle of arbitrary radius centred on a.
3. Pick a random point, b, on the circle.
4. With the compasses set to distance ab, mark two new points on the circle a distance ab from b.
5. Continue to mark points in this fashion until six equally-spaced points have been constructed around the outside of the circle.
6. Find the midpoint between each pair of adjacent points; project the line from a through this midpoint onto the circle and mark that.
7. This will give 12 equally-spaced points around the circle's circumference. Join them up.