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;

Extend of non-euclidean geometry form upon tradition space

Research on LDPC Codes Based on Euclidean Geometry;

At the same time,the duality propositions of the angular bisector,two perpendicular lines,the length of the line segment,the distance between a point and a line in Euclidean geometry,were also established.

Euclidean geometry is not only the leader of the civilization of ancient Greek but also the brilliant achievements of axiomatic approach in mathematics.

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.