Euclid & Lobatchevsky

[1] There is no royal road to geometry After the end of Archimedes, mathematical progress had stopped. Archimedes had developed mathematics to a point where no further advances could be made without the use of Algebra and uninflected geometry. History would have to wait seventeen centuries for the next major(ip) step. Archimedes had pointed the focussing to calculus or analysis, but there was no matchless there to number. The growing Roman Empire invaded Egypt, setting wind up to ships in Alexandria. The fire to the ships spread to the library and burnt-out fractional a million manuscripts-the repository of all ancient knowledge. What the flames missed, the Moslems plunder seven centuries later, scattering the heritage of Greece to the four winds. Lobatchevsky and Euclid both(prenominal) worked on a not so self-evident axiom that through a point in a condition plan merely one line can be drawn analogue to another line on the even. Euclid delineate the axiom as one that could not be proved. Lobatchevsky some(prenominal) years later move to prove this theory. He sight a non-euclidian geometry-pangeometry or complex number geometry which is not depicted on an ordinary flat plane of Euclid. Instead, it can be visualise on a psuedoshpere. even up though this tonic geometry was reasonable as valid as Euclids, early astronomers judgment Euclids theory more useful. euclidian geometry was capable of describing everything from paths of heavenly bodies to the sizes and shapes of dust.

Therefore, they thought if space is Euclidean it cannot be non-Euclidean. It wasnt ti ll the 19th century that Newtonian Physics,! which is found on a Euclidean interpretation of space, appeared to have umpteen problems. Albert Einstein, more than half a century later, erected a new system based on non-Euclidean geometry. This new system became a much simpler one to follow than Newtons system. opposed Euclid, Lobatchevsky received little obligingness and recognition during his life. Yet for everyplace two thousand years, no one had ever questioned Euclids geometry until Nicholas Lobatchevsky. If you want to get a full essay, order it on our website: OrderCustomPaper.com

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