Compass universally used as compass until the invention of the box-like compass with a 'dry' pivoting needle sometime around 1300. Originally, many compasses were marked only as to the direction of magnetic north, or to the four cardinal points (north, south, east, west). Later, these were divided, in China into 24, and in Europe into 32 equally spaced points around the compass card. For a table of the thirty-two points, see compass points. In the modern era, the 360-degree system took hold. This system is still in use today for civilian navigators. The degree system spaces 360 equidistant points located clockwise
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,