Leonhard euler achievement series

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    Leonhard Euler

    Swiss mathematician (1707–1783)

    "Euler" redirects here. For other uses, see Euler (disambiguation).

    Leonhard Euler (OY-lər;[b]German:[ˈleːɔnhaʁtˈʔɔʏlɐ]ⓘ, Swiss Standard German:[ˈleɔnhardˈɔʏlər]; 15 April 1707 – 18 September 1783) was a Swisspolymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential discoveries in many other branches of mathematics, such as analytic number theory, complex analysis, and infinitesimal calculus. He also introduced much of modern mathematical terminology and notation, including the notion of a mathematical function. He is known for his work in mechanics, fluid dynamics, optics, astronomy, and music theory.[7] Euler has been called a "universal genius" who "was fully equipped with almost unlimited powers of imagination, intellectual gifts and extraordinary memory".

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    Euler was not the first to identify \( e\) as an interesting mathematical constant (depending on what one takes "discover" to mean, the constant was discovered bygd either efternamn in the early 1600s or Bernoulli in the late 1600s), but he did man several important contributions to its study. In one of his most famous books, Introductio in Analysin infinitorum (1748), he showed that the infinite sum \[ \frac1{0!} + \frac1{1!} + \frac1{2!} + \cdots = \sum_{k=0}^{\infty} \frac1{k!} \] and the value of the limit \[ \lim_{n\to\infty} \left( 1+\frac1{n}\right)^n \] and the number \( a\) with the property that \[ \int_1^a \frac1{x} \, dx = 1 \] were all the same number, and called that number \( e \). He also gave an approximation to \( 23 \) decimal places. He was also the first to prove that \( e \) is irrational, by proving that its continued fraction is \[ e = [2;1,2,1,1,4,1,1,6,1,1,8,1,\cdots] = 2+\frac1{1+\frac1{2+\frac1{1+\frac1{1+\frac1{4+\frac1{\cdots}}}}}}. \] Since logisk numb

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    Leonhard Euler

    Leonhard Euler's father was Paul Euler. Paul Euler had studied theology at the University of Basel and had attended Jacob Bernoulli's lectures there. In fact Paul Euler and Johann Bernoulli had both lived in Jacob Bernoulli's house while undergraduates at Basel. Paul Euler became a Protestant minister and married Margaret Brucker, the daughter of another Protestant minister. Their son Leonhard Euler was born in Basel, but the family moved to Riehen when he was one year old and it was in Riehen, not far from Basel, that Leonard was brought up. Paul Euler had, as we have mentioned, some mathematical training and he was able to teach his son elementary mathematics along with other subjects.

    Leonhard was sent to school in Basel and during this time he lived with his grandmother on his mother's side. This school was a rather poor one, by all accounts, and Euler learnt no mathematics at all from the school. However his interest in mathematics had certainly been sparked