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  2. List of representations of e - Wikipedia

    en.wikipedia.org/wiki/List_of_representations_of_e

    The mathematical constant e can be represented in a variety of ways as a real number. Since e is an irrational number (see proof that e is irrational ), it cannot be represented as the quotient of two integers , but it can be represented as a continued fraction .

  3. 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 .

  4. Euler's identity - Wikipedia

    en.wikipedia.org/wiki/Euler's_identity

    Euler's identity is considered to be an exemplar of mathematical beauty as it shows a profound connection between the most fundamental numbers in mathematics. In addition, it is directly used in a proof [ 3 ] [ 4 ] that π is transcendental , which implies the impossibility of squaring the circle .

  5. List of mathematical proofs - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_proofs

    Gödel number. Gödel's incompleteness theorem; Group (mathematics) Halting problem. insolubility of the halting problem; Harmonic series (mathematics) divergence of the (standard) harmonic series; Highly composite number; Area of hyperbolic sector, basis of hyperbolic angle; Infinite series. convergence of the geometric series with first term ...

  6. Proof that e is irrational - Wikipedia

    en.wikipedia.org/wiki/Proof_that_e_is_irrational

    In 1840, Liouville published a proof of the fact that e 2 is irrational [10] followed by a proof that e 2 is not a root of a second-degree polynomial with rational coefficients. [11] This last fact implies that e 4 is irrational. His proofs are similar to Fourier's proof of the irrationality of e.

  7. Contributions of Leonhard Euler to mathematics - Wikipedia

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

    The 18th-century Swiss mathematician Leonhard Euler (1707–1783) is among the most prolific and successful mathematicians in the history of the field.His seminal work had a profound impact in numerous areas of mathematics and he is widely credited for introducing and popularizing modern notation and terminology.

  8. List of theorems - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems

    List of mathematical proofs; List of misnamed theorems; List of scientific laws; ... Euler's partition theorem (number theory) Euler's polyhedron theorem

  9. Pentagonal number theorem - Wikipedia

    en.wikipedia.org/wiki/Pentagonal_number_theorem

    For example, the diagram below shows n = 20 and the partition 20 = 7 + 6 + 4 + 3. Let m be the number of elements in the smallest row of the diagram (m = 3 in the above example). Let s be the number of elements in the rightmost 45 degree line of the diagram (s = 2 dots in red above, since 7