[1] There is no royal road to geometry After the devastation of Archimedes, mathematical progress had stopped. Archimedes had developed mathematics to a orientate where no further advances could be made without the use of Algebra and analytic geometry. History would have to wait seventeen centuries for the next major(ip) step. Archimedes had pointed the way to calculus or analysis, but there was no one there to number. The growing Roman Empire invaded Egypt, setting fire to ships in Alexandria. The fire to the ships spread to the library and burnt-out half a million manuscripts-the repository of all ancient knowledge. What the flames missed, the Moslems looted 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 only one line can be drawn parallel to another line on the plane. Euclid delineate the axiom as one that could not be proved. Lobatchevsky some(prenominal) years later tried to prove this theory. He sight a non-euclidian geometry-pangeometry or Imaginary geometry which is not depicted on an ordinary flat plane of Euclid. Instead, it can be visualise on a psuedoshpere. Even though this new geometry was reasonable as valid as Euclids, early astronomers judgment Euclids theory more useful. Euclidean 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 till the 19th century that Newtonian Physics, which is based on a Euclidean interpretation of space, appeared to have many 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. Unlike Euclid, Lobatchevsky received little obligingness and recognition during his life. Yet for over two thousand years, no one had ever questioned Euclids geometry until Nicholas Lobatchevsky.
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