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# The Controversial Both True and False The Fifth Postulate By Euclids

Euclids 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 Euclids 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 great work The Elements From the beginning Euclids fifth postulate also called the parallel postulate stood out from among Euclids other postulates The first four postulates are short brief and to the point whereas the fifth is longer and rather strange sounding The postulates are listed in The Elements as such 1 To draw a straight line from any point to another 2 To produce a finite straight line continuously in a straight line 3 To describe a circle with any center and distance 4 That all right angles are equal to each other 5 That if a straight line falling on two straight lines make the interior angles on the same side less than two right angles if produced infinitely meet on that side on which are the angles less than the two right angles Clearly there are dissimilarities between the last and the first four as Euclid must have been aware mainly in the length of the postulate In any case mathematicians of the time seeing that there was something strange about this parallel postulate set out to prove it by using only the first four postulates Many mathematicians among them Poisonous tried to define parallel lines in another way than Euclid However it was quickly observed that these definitions contained the fifth postulate as a premise Needless to say many great Greek mathematicians tried their hands at proving the postulate in a variety of ways they all failed Later the Arabic mathematicians who succeeded the Greeks

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