A new non-Euclidean distance was introduced to replace the Euclidean distance in the IPCM,and then a new fuzzy clustering,called novel improved possibilistic C-means(NIPCM)clustering was proposed.

A simple proof of finiteness of areas of asymptotic triangles in non-Euclidean geometry;

From the study of the parallel postulate to the establishment of the non-Euclidean geometry;

In this paper, the author queried a few conclusions in [1] , and elaborated different views on several problems, such as relations between non-Euclidean geometry and real space, relations between mathematical logic and thinking, the significance of Godel s second incompleteness theorem, and so on.