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 these straightedge and compass constructions have been shown to be logically impossible to perform. (The problems themselves, however, are solvable, and the Greeks knew how to solve them, "without" the constraint of working only with straightedge and compass.) The most famous of these problems, squaring the circle, otherwise known as the quadrature of the circle, involves constructing a square with the same area as a given circle using only straightedge and compass. Squaring the circle has been proven impossible, as it involves generating a transcendental number, that is, . Only certain algebraic numbers can be constructed with ruler and compass