Points of the compass Points of the compass The points of the compass mark the divisions on a compass, which is primarily divided into the four cardinal directions: north, south, east, and west. These points are further subdivided by the addition of the four intercardinal (or ordinal) directions—northeast (NE), southeast (SE), southwest (SW), and northwest (NW)—to indicate the eight principal winds. In meteorological usage, further intermediate points between the cardinal and intercardinal directions, such as north-northeast (NNE) are added to give the sixteen points of a compass rose. At the most complete division are the full thirty-two points of the mariner's compass, which adds
Straightedge and compass construction More formally, the only permissible constructions are those granted by Euclid's first three postulates. It turns out to be the case that every point constructible using straightedge and compass may also be constructed using compass alone. The ancient Greek mathematicians first conceived straightedge and compass constructions, and a number of ancient problems in plane geometry impose this restriction. The ancient Greeks developed many constructions, but in some cases were unable to do so. Gauss showed that some polygons are constructible but that most are not. Some of the most famous straightedge and compass problems were proven impossible by Pierre Wantzel