11/7/2023 0 Comments Euclidean geometry definition![]() Not a great proof and written after it was proven that this could not be proved.Īs I understand it, the postulates/axioms are assumptions and they are used to construct theorems. On a side note, in 1890, Charles Dodgson (aka Lewis Carroll author of Alice in Wonderland) published a book with a "proof" of the parallel postulate using the first 4 postulates. We can see different versions of systems where the parallel postulate is false by assuming that either there are no parallel lines, or that for any line and point not on a line there are an infinite number of parallel lines. Later (1868) it was proved that the two systems were equally consistent and as consistent as the real number system. In the late 19th century (approximately 1823), three different mathematicians (Bolyai, Lobachevsky and Gauss) proved independently that there was a different system that could be used that assumed the 5th postulate was incorrect. Some really great proofs were created by mathematicians trying to prove the parallel postulate. Mathematicians kept trying to prove that the 5th postulate (commonly known as the parallel postulate) could be proved from the first four postulates and thus was unnecessary. ![]() There was a big debate for hundreds of years about whether you really needed all 5 of Euclid's basic postulates.
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