Compass has a half-life of only about 12 years, so a compass that contains 120 mCi of tritium when new will contain only 60 when it is 12 years old, 30 when it is 24 years old, and so on. Consequently, the illumination of the display will fade. Mariners' compasses can have two or more magnets permanently attached to a compass card, which moves freely on a pivot. A "lubber line", which can be a marking on the compass bowl or a small fixed needle, indicates the ship's heading on the compass card. Traditionally the card is divided into thirty-two points
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,