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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. Euler's identity - Wikipedia

    en.wikipedia.org/wiki/Euler's_identity

    In mathematics, Euler's identity [note 1] (also known as Euler's equation) is the equality + = where e {\displaystyle e} is Euler's number , the base of natural logarithms , i {\displaystyle i} is the imaginary unit , which by definition satisfies i 2 = − 1 {\displaystyle i^{2}=-1} , and

  4. 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 ...

  5. 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.

  6. List of representations of e - Wikipedia

    en.wikipedia.org/wiki/List_of_representations_of_e

    Euler's identity; Euler's formula; ... Euler proved that the number e is represented as the infinite simple continued fraction [1] ... as discovered by Harlan Brothers.

  7. 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.

  8. Euler's constant - Wikipedia

    en.wikipedia.org/wiki/Euler's_constant

    Discovered: 1734: By: Leonhard Euler: ... Euler's constant ... An approximation of the average number of divisors of all numbers from 1 to a given n.

  9. List of mathematical constants - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_constants

    Explanations of the symbols in the right hand column can be found by clicking on them. List. Name Symbol Decimal expansion Formula ... Euler's number 2.71828 18285 ...