
Chapter 20
Regular Polygons
We return with more sophisticated weapons to the time-honoured problem of ruler-
and-compass construction, introduced in Chapter 7. We consider the following ques-
tion: for which values of n can the regular n-sided polygon be constructed by ruler
and compass?
The ancient Greeks knew of constructions for 3-, 5-, and 15-gons; they also knew
how to construct a 2n-gon given an n-gon, by the obvious method of bisecting the
angles. We describe these constructions in Section 20.1. For about two thousand
years little progress was made beyond the Greeks. If you answered Exercises 7.16
or 7.17 you got further than they did. It seemed ...