Compass-and-straightedge Construction And Three Geometric Problems

Construction is an indispensable part of geometric problems and methods.Compass-and-straightedge construction has its charm that can not be ignored as the basicmapping method. There is a certain necessity both in the theoretical and practical value ofcompass-and-straightedge construction. A systematic research has been done on this issue inthis article. The content mainly consists of two parts:First, it introduces the origin of compass-and-straightedge construction, including thedevelopment of Chinese ancient compass-and-straightedge construction and ancient Greekcompass-and-straightedge construction. Then it describes the reason why ancient Greekmathematician limit this method., and it also introduces how to practice this method in middleschool mathematics class. Finally the article illustrates the application in the teaching ofmiddle school maths with several examples.Second, it introduces the content and origin of the three geometric problems.And itproves that the problems which can not be solved with compass and straightedge. It embodiesthe ideas of solving the problem of geometric by algebra method.It can get the conclusion thatthe collection of compass-and-straightedge construction is algebraic number based on theresearch of the three geometric problems.Then it gets the condition of the roots of cubicequation than can’t construction with compass and straightedge.Thus it proves the problemscan not be solved with compass and straightedge. Finally, it describes the methods of threegeometric problems without compass and straightedge.The three geometric problems havebeen solved perfectly.