#HOW DID PYTHAGORAS DISCOVER HIS THEOREM FULL#

Getting back to the Pythagorean rule, I think the first task is to ask why ancient peoples were led to study triangles. When, in the same situation, I read in his manuscript things that people would write today (adjusting for notation), I feel justified in believing I can hear him 'speak'. I take math to be a fixed set of problems and results, independent of culture just as metallurgy is a fixed set of facts that can be used to analyze ancient swords. I am aware that historians would say I am not reading him for what he says but am distorting his words using my modern understanding of math. Here he was working out a Riemann sum for an integral, here he was making the irritating estimates needed to establish convergence. I was reconstructing a rich picture of Archimedes based on my prior. I knew how my mathematical contemporaries reasoned and his whole way of doing math fit hand-in-glove with my own experience. My personal experience reading Archimedes for the first time illustrates my bias: after getting past his specific words and the idiosyncrasies of the mathematical culture he worked in, I felt an amazing certainty that I could follow his thought process. Of course this is also the fundamental reason why histories of the same event written at various times in later centuries differ so much. Indeed, Rushdie quotes his Cambridge Professor Hibbert saying 'You must never write history until you can hear the people speak'.

#HOW DID PYTHAGORAS DISCOVER HIS THEOREM FULL#

Of course primary sources are infinitely better than secondary ones, but everyone has built up their personal prior on human behavior and human culture and uses this to expand the meager sources that survive into a full blown reconstruction of some events. Scholars have the illusion when they are relying only on primary sources that they not making significant inferences but I believe they are mistaken. Even in our own lifetimes, we rely on faulty and selective memories in reconstructing events. We never have full knowledge of any past part of space-time. My view of history in general, not just protohistory, is that it is always an exercise in Bayesian inference. However, all is not speculation and, for great help in all that a real scholar of the History of Math might study, I want to thank Jens HГёyrup for all his help. But that's what I want to do in this blog. The full history of Pythagoras's rule is a perfect example of a problem on which one can only speculate. All this work belongs to what AndrГ© Weil called 'protohistory', an attempt to be scholarly when surviving documents are not only sparse but also possibly unrepresentative of a tradition, and totally absent from other cultures. But because this rule may be described in math-talk as the first 'non-trivial' mathematical theorem to be discovered, there has been extensive debate about when and where it was first found, whether it was discovered independently in several places and how it was found. Due to the wholesale destruction of documents in China in the Qin dynasty (221-206 BCE), the earliest records we have for the rule from China date from the second century BCE. After the Babylonians it next appears in extant records in Indian Vedic altar construction manuals, composed and transmitted orally as early as 800 BCE. In any case, we don't know if Pythagoras proved it or not. I am calling it a rule, not a theorem, following Jens HГёyrup's suggestion, because it appears as a rule for connecting these lengths, not a theorem, in most of its early history. The earliest extant documents that show knowledge of the rule relating the lengths of the three sides of a right triangle, that is traditionally named after Pythagoras, are Babylonian tablets dating from the centuries around Hammurabi's time, c.

How did pythagoras discover his theorem