Three Geometric Problems Of Ancient Greek Research Course

Three geometric problems is a important chapter in the history of mathematics and isone of the concerns in the mathematic history. So, studying the three geometric problemshas a certain theoretical significance and practical value. This paper on this issue does asystematical study. The main content is devided into the following sections:Firstly, through impecting three geometric problems,and drawing with ruler andcompass,s history, I think their appearance is closely related to people,s production andlife,s background at that time.Secondly, I describe the not drawing with ruler and compass of the three geomet-ric problems in detail, and point out mathematicians have solved the three geometricproblems: trisection angle, transforming a circle into asquare and cube,square with dif-ferent methods and means. Their solving the problems promote the futher developmentof mathematical thoughts.Thirdly, I simply describe the origin of the number which can be constructed; summa-rize Lagrange,impotant thoughts about the solution of algebraic equations; use the casex¹⁷ 1 = 0 to illustrate Gauss,solution of cyclotomic equation methods and thoughts,so, I summarize a necessary and sufcient condition of drawing with ruler and compass,which reveals the main thoughts of soloving the three geometric problems with algebraicmethods.Fourly, I describe Wantzel,study unsolvability of the three geometric problems indetail, and find his mapping problem,cure is the same as the Gauss,, however, theirdiference is Gauss is the use of cyclotomic equation to solve the positive n edge shape,smapping problems with ruler and compass, but Wantzel is through equation groups which are made up of a series of interrelated two equations to solve problems of the number whichcan be constructed. Futher, I find Wantzel,methods just make up for Gauss,solving thepositive n edqe shape,deficiencies. In addition, I summarize Galois,solvability problemsand his main throught. He proves the three geometeic problems impossibility using thethought of group theory, which draws a conclusion: the equivalence drawing with rulerand compass.