Points of the compass limit of the compass point. By the middle of the 18th century, the 32-point system had been further extended by using half- and quarter-points to give a total of 128 directions. These fractional points are named by appending, for example east, east, or east to the name of one of the 32 points. Each of the 96 fractional points can be named in two ways, depending on which of the two adjoining whole points is used, for example, NE is equivalent to NbEN. Either form is easily understood but alternative conventions as to correct usage developed in different countries and
Straightedge and compass construction condition for regular polygons is also necessary. Then in 1882 Lindemann showed that formula_1 is a transcendental number, and thus that it is impossible by straightedge and compass to construct a square with the same area as a given circle. All straightedge and compass constructions consist of repeated application of five basic constructions using the points, lines and circles that have already been constructed. These are: For example, starting with just two distinct points, we can create a line or either of two circles (in turn, using each point as centre and passing through the other point). If we draw