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 parabolic interpolation was created by Liu Zhou (刘焯) for dealing with the irregular movement of celestial body in 600 AD. As a numerical method, Liu's interpolation led the mainstream of traditional Chinese calendar-making system thereafter. The characters of mathematical astronomy of Chinese and western differ greatly in their algorithms. Chinese people intended to invent a numerical method such as the interpolation instead of a celestial model as Ptolemy's epicycle-deferent system. Based on a discussion of the evolution of Chinese solar motion theory around the 7th century, the present paper will illustrate why Chinese raised such an idea of interpolation, how they made use of this kind of method, and if it was developed independently.

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.