Movement Axiom Of Euclid Geometric System And High School Maths Education

During the continuous adjustment of math curriculum in high school,it is always a controversial question that how to deal with the geometric axioms in the textbooks.This article only discussed "edge, corner,edge" theorem.In the Hilbert axiom system it is just an axiom (contract Axiom),whereas in Euclidean geometry systems it is proved by sports intuitive,which was later proved to be a lot of criticism for being not strict.After the abolition of this proof in textbooks,it is no longer involved in sports intuitive,but the effect is bad.Actually,The concept of sport can be strictly axiomatic,and it is not difficult.The purpose of this article is to tell that sport intuitive is necessarily involved in congruent teaching exercise in fact,and it has been in Euclidean geometry System.It will not only help teachers to understand the concept of sport in this part of the contents but also be feasible and beneficial for teaching.Especially because of using sports intuitive,Euclid's "Elements" is easier for beginners to accept,and becomes the first entry in geometry.But Hilbert's "basic geometry" can not be that.The basic concept in Euclid's system is sport and the contract is the result of graphics when being moved to be superimposed,so it is a derivative concept from sport.However,Hilbert opposed.He held that the basic concept is the contract of graphics,and sports are the actions of the contracts of graphics being mutually superimposed ,so sports are from the concept of contract.We know that both are correct,but in high school math education now,the concept of sport is clearly more suitable for students to understand the concept than the contract.We proved the compatibility,independence,and completeness in the axiomatic system which was from the replacement from contracts axiom to sports axiom,and put out the strict definition and the related content of plane and space sport groups.In the end,we show three examples to prove that it does not affect the completeness when the replacement occurs.The introduction of sports axiom shows that the language of Euclidean geometry axioms are more conducive to teach and easily for students to accept.Some issues will be illuminating after the introduction.