euclid's 5th postulate

Euclid’s Fifth Postulate One of the most fascinating aspects of Mathematics is that there exist statements that are both true and false. Perhaps the most famous of these is Euclid’s controversial fifth postulate. Throughout history, almost from the postulate conception, mathematics have tried to prove or disprove it. Actually, it seems that even Euclid himself did not entirely trust the postulate, for he avoided using it as long as he could in his …

…main classes of geometry: Euclidean and Non-Euclidean, which consists of both the Bolyai-Lobaschevsky and Reimann models. It has been sufficiently proven that Euclid’s fifth postulate can be both true and false. By assuming it true, one can generate the geometrical world know as Euclidean Geometry in which no contradiction has arisen. Likewise, by assuming a different theory of parallels, one can generate another, quite separate geometrical world in which no contradiction has been found.