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  2. Euler's identity - Wikipedia

    en.wikipedia.org/wiki/Euler's_identity

    Euler's identity is a direct result of Euler's formula, published in his monumental 1748 work of mathematical analysis, Introductio in analysin infinitorum, [16] but it is questionable whether the particular concept of linking five fundamental constants in a compact form can be attributed to Euler himself, as he may never have expressed it.

  3. Euler's formula - Wikipedia

    en.wikipedia.org/wiki/Euler's_formula

    Euler's formula is ubiquitous in mathematics, physics, chemistry, and engineering. The physicist Richard Feynman called the equation "our jewel" and "the most remarkable formula in mathematics". [2] When x = π, Euler's formula may be rewritten as e iπ + 1 = 0 or e iπ = −1, which is known as Euler's identity.

  4. File:Illustration of Euler Identity.pdf - Wikipedia

    en.wikipedia.org/wiki/File:Illustration_of_Euler...

    Microsoft Word - Illustration of Euler.doc; Date and time of digitizing: 15:20, 21 September 2008: Software used: PScript5.dll Version 5.2: File change date and time: 15:20, 21 September 2008: Conversion program: Acrobat Distiller 6.0 (Windows) Encrypted: no: Page size: 612 x 792 pts (letter) Version of PDF format: 1.4

  5. List of formulae involving π - Wikipedia

    en.wikipedia.org/wiki/List_of_formulae_involving_π

    Download as PDF; Printable version; ... The buckling formula: = ... (Euler's identity) The following equivalences are true for any complex ...

  6. File:E-to-the-i-pi.svg - Wikipedia

    en.wikipedia.org/wiki/File:E-to-the-i-pi.svg

    This mathematical term forms part of an identity, a special case of Euler's formula, written = ⁡ + ⁡ (). Setting x {\displaystyle x} to a value of π {\displaystyle \pi } , as with the above term, Euler's formula reduces to a famous equation relating seven important mathematical symbols (and none that are unimportant!), namely e i π + 1 ...

  7. Introductio in analysin infinitorum - Wikipedia

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

    Then in chapter 8 Euler is prepared to address the classical trigonometric functions as "transcendental quantities that arise from the circle." He uses the unit circle and presents Euler's formula. Chapter 9 considers trinomial factors in polynomials. Chapter 16 is concerned with partitions, a topic in number theory.

  8. 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 ...

  9. List of mathematical identities - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical...

    Bézout's identity (despite its usual name, it is not, properly speaking, an identity) Binet-cauchy identity; Binomial inverse theorem; Binomial identity; Brahmagupta–Fibonacci two-square identity; Candido's identity; Cassini and Catalan identities; Degen's eight-square identity; Difference of two squares; Euler's four-square identity; Euler ...