mardi 26 février 2013

Die Schweiz (Switzerland)

Switzerland is a small landlocked European country of 41 285 square kilometers divided by 26 cantons with Bern as the capital city, and Zurich as the largest one. It is bordered by Germany to the north, France to the west, Italy to the south, and Austria and Liechtenstein to the east.The country has four official languages: German, French, Italian and Romansh, it is more a confederation than a cultural country, and has for motto:  "Unus pro omnibus, omnes pro uno" (One for all, all for one). The Swiss population is around eight millions and the government is a federation, a federal republic and a direct democracy. Their currency is the Swiss Franc, Switzerland is not part of the European UnionSwitzerland is known worldwide for watches, chocolate, dairy products like cheese, then banking, tourism, postcard places, skiing, and even the Swiss army knife is very famous.

Pictures describing Switzerland



  
 

The world’s most famous Swiss mathematician is Leonhard Euler.
Considered to be the superior mathematician of the 18th century, Euler also worked in Mechanics, Fluid dynamics, Optics, and Astronomy.

He is the only mathematician to have two numbers named after him, the very important Euler's Number in calculus, e, approximately equal to 2.71828, and the Euler-Mascheroni Constant γ (gamma) sometimes referred to as just "Euler's constant", approximately equal to 0.57721. It is not known whether γ is rational or irrational !!
Euler demonstrated the existence of a line called the Euler line, which is a line formed, in any triangle, by the three points, the first one made with the intersection of the heights,the second one, with the intersection of the perpendicular bisectors, and the last one, the intersection of the medians.
He introduced the concept of a function and was the first to write f(x) to denote the function f applied to the argument x.
Euler introduced The Greek letter Σ for summations, and the letter π, was popularised by Euler, whereas it didn't originate from him.

The Seven Bridges of Königsberg is one of the most important mathematical problems in history. Its negative resolution was completed by Euler, in 1735. The city of Königsberg in Prussia (now Kaliningrad, Russia) was set on both sides of the Pregel river, and included two large islands which were connected to each other and the mainland by seven bridges. The problem consisted of finding a way to walk all over the city, crossing all the bridges, but each bridge only once. The resolution of this problem helped the foundations of graph theory and prefigured the idea of topology.


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