浅谈第五公设的产生及其对数学的影响

AbstractEuclid's fifth postulate is the intersection of a straight line and two other straightlines in the plane.If the sum of two inner angles on one side of the plane is less thantwo right angles,then the two straight lines will intersect on this side after an infiniteextension.Due to the complexity of the content and narrative of the Fifth Post,thecontinuous research and discussion on it by later generations has aroused manycontroversies.For more than 2,000 years,many scholars have tried unsuccessfully touse the rest of the postulates and inferences in the Euclid's Elements,but haveobtained some propositions equivalent to the fifth postulate.Later,some newpropositions that were different from Euclidean geometry were derived,which led tothe emergence of non-Euclidean geometry.Euclid relied only on formal thinking andformed a system through graphical evidence,and used it first in the 29th proposition.Due to certain contradictions of the fifth postulate and its independence from otheraxioms,definitions,and postulates,mathematicians of the past dynasties activelyexplored,tried to make up for it,or tried to expand new fields,which greatlydeveloped mathematics.The most significance of the fifth postulate to thedevelopment of geometry comes from the negation of the fifth postulate,that is,thebirth of non-euclidean geometry.Key Words:Mathematics,The fifth postulate,Non-euclidean geometry,Geometry