Compass rose two adjacent cardinal directions. For example, North-by-east (NbE) is one quarter wind from North towards East, Northeast-by-north (NEbN) is one quarter wind from Northeast toward North. Naming all 32 points on the rose is called "boxing the compass". The 32-point rose has the uncomfortable number of 11° between points, but is easily found by halving divisions and may have been easier for those not using a 360° circle. Using gradians, of which there are 400 in a circle, the sixteen-point rose will have twenty-five gradians per point. Linguistic anthropological studies have shown that most human communities have four points of
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,