Many mathematicians (amongst the Greeks, the Arabs, Europeans) believed that the 5th postulate actually was not necessary, that it could have been proven as a theorem, but up to today its proof has not been figured out. Some people believe the Euclid originally started off with only 4 postulates and later only added the fifth one, when he realized it would be necessary. These mathematicians eventually discovered Hyperbolic Geometry! The first 28 theorems in Euclid’s book, the Elements, do not use the parallel postulate for their proof. Euclid’s fifth postulate contributed to the development of non-Euclidean Geometry because in trying to prove it all of these mathematicians independently discovered a non-Euclidean geometry and by doing so had come to the same conclusion that the Parallel Postulate cannot be proven from the other four postulates of Euclid’s Geometry. The consideration of alternatives to Euclid’s parallel postulate resulted in the development of non-Euclidean geometries.įor more than 2000 years, mathematicians tried proving the 5 th postulate using only the first four postulates, but were unsuccessful and ended up with new geometry. The fifth postulate is often called the Parallel Postulate even though it does not specifically talk about parallel lines it actually does deal with ideas of parallelism. The fifth postulate-the “parallel postulate”-however, became highly controversial. Euclid’s first four postulates have always been readily accepted by mathematicians.
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