Abstract:

Abstract: Based on expressions of Gauss projection by complex numbers, the conformal latitude by complex numbers was introduced to solve the singularity problem of isometric latitude in polar regions. Secondly, conformal colatitude by complex numbers was introduced on the basis of conformal latitude by complex numbers, with the polar point taken as the origin of coordinates in Gauss projection, the non-singular formula of Gauss projection in polar regions by complex numbers was set up. Finally, compared with traditional power series and expressions by complex numbers of Gauss projection, the non-singular formula proved to be highly accurate. The new expression of Gauss projection in polar regions could overcome imperfection of zonation of traditional Gauss projection, which makes Gauss Projection a uniform integrated form in polar regions.

Key words: Key words: Gauss projection, non-singular formula, complex numbers, polar regions, colatitude