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Trigonometry of Rational Numbers

Victor Aguilar

posted on 20 January 2016

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Brahmagupta invented the additive identity zero about a millennium after Euclid.  A rigorous definition for the field of rational numbers was within his grasp!  It was only the existence of irrational numbers that stayed his hand.  Trigonometry to six decimal digits of accuracy was possible in Brahmagupta’s day, but it would have required that he redefine the unit of angle.  Also, he would have had to come to grips with the fact that Dedekind was still a millennium in his future, so he needed to just get busy studying trigonometry within the context of the field of rational numbers.