Note. The foregoing method, using the law of cosines,
also works if the polygon has an even number of sides, say
2n + 2 sides, but one minor change is needed. There are
now 2n + 1 segments from a given vertex to the remaining
vertices. One of these is a diameter, and the other 2n can be
arranged in pairs by coupling each segment with its mirror
image in that diameter. However, we do not give further details
because the proof presented in Section 7 is more elementary.