The Chinese calendar is a lunisolar calendar based on astronomical events, not arithmetical rules. Days begin at civil midnight. Months are lunar, beginning on the day of the new moon and ending on the day before the next new moon. Years contain 12 or 13 such months, with the number of months determined by the number of new moons between successive winter solstices. The details of the Chinese calendar have varied greatly—there have been more than 50 calendar reforms—since its inception in the fourteenth century B.C.E.; some of its history, in particular its effect on the development of mathematics in China, is described in [13]; other historical details can be found in [5] and [16].