sobota 14. dubna 2012

Why geometry is taught

The history of Mathematics as we know it started in the 5th century BC in antic Greece, where philosophers examined geometry and postulated things like Pythagorean triangle. And for example architecture benefited from the geometry and it allowed construction of great buildings like Pantheon or Roman Colosseum.
But in the 5th century AD west Roman empire collapsed and western Europe sank in the darkness. This epoch is characterized by Romanesque art, which employs massive walls and small windows because otherwise the building would collapse.
However, in the 11th century Crusaders conquered Jerusalem and they have been amazed by the local architecture and decided to transport local "the true Gods" architecture back to home. Hence they have pillaged libraries and acquired many translations of antique books in Arabian language. The imported architecture is now called Gothics and it was possible build such elegant and high buildings only because the information from ancient Rome and Greece were recovered.
As more and more people obtained access to the ancient books a new epoch called Renaissance emerged. In translation Renaissance means reborn, reborn of antique culture. Since antique mathematics focused mostly on geometry, all new observations were proved using geometry. This promoted progress in astronomy, which studies trajectories of planets, and optics. Hence Kepler postulated hypothesis that planets follows ellipsoid trajectories and Tycho de Brahe designed a new type of telescope.
But then it looked like everything that can be easily proved using geometry was already proved and a new way how to prove things emerged independently from Newton and Leibniz in the 17th century. This new method, integrals, favored advances in mechanics and led to introduction of steam machines, combustion engines and atom energy.
Nowadays no one proves things using geometry because integrals are easier to use. However, no one likes to throw out 23 centuries of research and still geometry is easier to understand than integrals - just recall how integrals were explained - like an are under the curve...         

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