Points of the compass "X "al" Y" (X to Y) or "X "per" Y" (X by Y). There are no irregularities to trip over; the closest principal wind always comes first, the more distant one second, for example: north-by-east is ""Quarto di Tramontana verso Greco""; and northeast-by-north is ""Quarto di Greco verso Tramontana"". The table below shows how the 32 compass points are named. Each point has an angular range of 11.250 degrees where: middle azimuth is the horizontal angular direction (from north) of the given compass bearing; minimum is the lower angular limit of the compass point; and maximum is the upper angular
Siegel's theorem on integral points Siegel's theorem on integral points In mathematics, Siegel's theorem on integral points is the 1929 result of Carl Ludwig Siegel, that for a smooth algebraic curve "C" of genus "g" defined over a number field "K", presented in affine space in a given coordinate system, there are only finitely many points on "C" with coordinates in the ring of integers "O" of "K", provided "g" > 0. This result covers the Mordell curve, for example. This was proved by combining a version of the Thue–Siegel–Roth theorem, from diophantine approximation, with the Mordell–Weil theorem from diophantine geometry (required in Weil's version,