Euler General Study Of Spherical To Planar Projection

In order to draw the Russian map,Euler first introduced the surface parameters coordinates,the spherical plane projection problem into mathematical analysis.He defines that the conformal mapping is equivalent to the dominance mapping plus the conformal mapping,which for the first time proves that the sphere can not be conformally projected onto the plane and the general solution of the spherical to the plane beacon projection is obtained.This work not only provides the basis for his drawing of the Russian map,but also establishes the basis for Gaussian to establish conformance mapping on any two surfaces.On the basis of studying and analyzing the original literature,this paper explores the causes of Euler’s spherical-to-plane projection theory,analyzes the specific ideas of Euler spherical projection work,combs the general solution of spherical to planar projection,and obtains Euler to create spherical Plane projection of the road map,and finally the Euler projection work and Gauss in 1825 published "will be given a given surface projection to another surface and make the smallest part to maintain a similar general solution" paper for comparison,found that both in the ideological and Methods are reflected in the idea of Euler,and Euler to study the spherical plane to the general solution is similar to the solution.