日历中一种周期现象的解析

The analysis of a cycle phenomenon in the calendar

指出日历中的国庆日与中秋节重合这种现象发生的周期性.从公历和农历的历法依据——回归年和朔望月出发,利用辗转相除法以及连分数等数学方法对农历的置闰月规律加以推演,进而得出两种历法运行的会合周期.同时对其会合周期的差异性加以分析.

The paper points out cyclicity of the coincidence phenomenon about the National Day and the Mid-Autumn Festival. Based on the solar calendar and lunar calendar -- tropical year and lunar month, in combination with mathematical methods like the successive division and continued fractions and so on, the laws of intercalary month in the lunar calendar can be deduced and then the synodic period of the two calendars should be concluded. Also, to begin with setting the cycle on the size of the month in the lunar calendar, the differences of the synodic period of the two calendars are analyzed.