This paper established two triangle inequalities containing angular parameter and the fundamental inequality of triangle was strengthened.

The displacement Angle of strata has a great bearing on the size of coal pillar for protection of buildings on very thick unconsolidated layers, and has a great economic potentials.

These methods can be divided into three: (1) method based on progressive mesh (2) method based on sphere relaxation (3) conformal method. The three methods have their own advantages and shortcomings.