Points of the compass 32-wind compass rose is yielded from the eight principal winds, eight half-winds and sixteen quarter-winds combined together, with each compass direction point at an ° angle from the next. In the mariner's exercise of boxing the compass, all thirty-two points of the compass are named in clockwise order. The traditional compass rose of eight winds (and its 16-wind and 32-wind derivatives) was invented by seafarers in the Mediterranean Sea during the Middle Ages (with no obvious connection to the twelve classical compass winds of the ancient Greeks and Romans). The traditional mariner's wind names were expressed in Italian, or more
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,