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  2. e (mathematical constant) - Wikipedia

    en.wikipedia.org/wiki/E_(mathematical_constant)

    The number e is a mathematical constant approximately equal to 2.71828 that is the base of the natural logarithm and exponential function.It is sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can invite confusion with Euler numbers, or with Euler's constant, a different constant typically denoted .

  3. List of representations of e - Wikipedia

    en.wikipedia.org/wiki/List_of_representations_of_e

    A unique representation of e can be found within the structure of Pascal's Triangle, as discovered by Harlan Brothers. Pascal's Triangle is composed of binomial coefficients, which are traditionally summed to derive polynomial expansions. However, Brothers identified a product-based relationship between these coefficients that links to e.

  4. Proof that e is irrational - Wikipedia

    en.wikipedia.org/wiki/Proof_that_e_is_irrational

    The number e was introduced by Jacob Bernoulli in 1683. More than half a century later, Euler, who had been a student of Jacob's younger brother Johann, proved that e is irrational; that is, that it cannot be expressed as the quotient of two integers.

  5. Contributions of Leonhard Euler to mathematics - Wikipedia

    en.wikipedia.org/wiki/Contributions_of_Leonhard...

    Euler's great interest in number theory can be traced to the influence of his friend in the St. Peterburg Academy, Christian Goldbach. A lot of his early work on number theory was based on the works of Pierre de Fermat, and developed some of Fermat's ideas. One focus of Euler's work was to link the nature of prime distribution with ideas in ...

  6. History of calculus - Wikipedia

    en.wikipedia.org/wiki/History_of_calculus

    The discovery of Euler's number e, and its exploitation with functions e x and natural logarithm, completed integration theory for calculus of rational functions. One prerequisite to the establishment of a calculus of functions of a real variable involved finding an antiderivative for the rational function f ( x ) = 1 x . {\displaystyle f(x ...

  7. List of examples of Stigler's law - Wikipedia

    en.wikipedia.org/wiki/List_of_examples_of_Stigler...

    Euler's number: the "discovery" of the constant itself is credited to Jacob Bernoulli, but it is named after Leonhard Euler. Euler's formula: an equivalent formula was proved by Roger Cotes 30 years before Euler published his proof.

  8. Introductio in analysin infinitorum - Wikipedia

    en.wikipedia.org/wiki/Introductio_in_analysin...

    Euler's number e corresponds to shaded area equal to 1, introduced in chapter VII. Introductio in analysin infinitorum (Latin: [1] Introduction to the Analysis of the Infinite) is a two-volume work by Leonhard Euler which lays the foundations of mathematical analysis.

  9. Leonhard Euler - Wikipedia

    en.wikipedia.org/wiki/Leonhard_Euler

    Leonhard Euler (/ ˈ ɔɪ l ər / OY-lər; [b] German: [ˈleːɔnhaʁt ˈʔɔʏlɐ] ⓘ, Swiss Standard German: [ˈleɔnhard ˈɔʏlər]; 15 April 1707 – 18 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician, and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of ...