The Gauss's Researches On The General Solutions Of The Conformal Projections

From the Greek time to the early 19th century, due to the needs of military and economic, mathematicians and geodetic scientists from all countries have been looking for a method that make the Earth conformally projected onto a plane, therefore conformal projection problem occuped an important position in the history of mathematics as well as geodesy history. About 1816, Gauss began the research work which to measure the radians of Hanover, proposed the problem that how to establish conformal projection between any two surfaces, in 1822, he put forward its general solution, and published this results in the title of "General Solution of the Problem to so represent the Parts of one Given Surface upon another Given Surface that the representation shall be similar, in its smallest Parts, to the Surface represented" in 1825.Based on the study and analysis of the original document and research literature, explore the fuse which caused Gauss to consider the general solution of establishing the conformal projection between any two surfaces, analysis the ideas of Gauss translated the conformal projection problem into the mathematical problem, card the specific steps of the Gauss about the conformal projection's general solution, analysis the five examples given in Gauss's 1825 paper, and found that the five examples distinctive, and four of them contacted closely, restore the thought which Gauss wanted to express by this five examples is that any research on the conformal projection between any two surfaces can be simplified to the conformal projection between the two planes, and finally point out that Gauss's this work have an important significance for his later the formation of intrinsic differential geometry theoryhis and the performace of geodetic work.