This method is based upon euclidean distance, first by determining the explosive s ideal solution and negative - ideal solution, then by considering the euclidean distance between the explosive solution and the ideal solution and the negative - ideal solution synthetically.

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.

The algorithm is based on a modification of Euclid s algorithm.

The development of calculus was based on not very strict but practical thought instead of Euclid s strict thought.

wA mathematical model so called “Poincaré Model” is introduced to solve these problems by using the theorems of Euclidean geometry stead of Non Euclidean geometry.

Examination of the possible world in Europead s geometrical system based on pure deduction;