Chapter 20Regular 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 question: for which values of n can the regular n-sided polygon be constructed by ruler and compass?
The ancient Greeks knew 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 ‘obvious’ that the Greeks had found all the constructible regular ...
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