There are only two kinds of non-isomorphic consecutive vertex labelings of octahedron, and each of them can be deduced from the other. There is an algorithm to construct consecutive edge labelings. It is shown that there exist many non-isomorphic complementary consecutive edge labelings of octahedron.

The first approach to the history of mathematics in China led by Li Yan (1892-1963) and Qian Baocong (1892-1974) featured discovering what mathematics had been done in China's past. From the 1970s on, Wu Wen-tsun and others shifted this research paradigm to one of recovering how mathematics was done in ancient China. Both approaches, however, focus on the same problem, that is mathematics in history. The theme of the third approach is supposed to be why mathematics was done. Combining this approach with the former two, the research paradigm will be improved from one of mathematics in history to that of the history of mathematics.

日食的食差是月亮的视差对日食食甚时刻月亮到黄白交点之距离的修正值。从形式上看，其理论模型与中国古代的传统算法几乎没有任何相似之处。为了与理论算法进行比较，成功地将薮内清建立的理论模型简化为以太阳的黄经与时角为自变量的二元函数；同时，重构了传统算法的数学模型。在此基础上，比较了传统算法与理论算法的异同，得出的结论是：两者的数学模型是相似的、计算结果是近似的。以现代科学的标准来看，中国古代日食食差算法的数学模型是合理的、有效的。