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  2. Proof that π is irrational - Wikipedia

    en.wikipedia.org/wiki/Proof_that_π_is_irrational

    Another proof, which is a simplification of Lambert's proof, is due to Miklós Laczkovich. Many of these are proofs by contradiction . In 1882, Ferdinand von Lindemann proved that π {\displaystyle \pi } is not just irrational, but transcendental as well.

  3. List of mathematical constants - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_constants

    For example, the constant π may be defined as the ratio of the length of a circle's circumference to its diameter. The following list includes a decimal expansion and set containing each number, ordered by year of discovery. The column headings may be clicked to sort the table alphabetically, by decimal value, or by set.

  4. Euler's identity - Wikipedia

    en.wikipedia.org/wiki/Euler's_identity

    is pi, the ratio of the circumference of a circle to its diameter. Euler's identity is named after the Swiss mathematician Leonhard Euler . It is a special case of Euler's formula e i x = cos ⁡ x + i sin ⁡ x {\displaystyle e^{ix}=\cos x+i\sin x} when evaluated for x = π {\displaystyle x=\pi } .

  5. Gelfond's constant - Wikipedia

    en.wikipedia.org/wiki/Gelfond's_constant

    In mathematics, the exponential of pi e π, [1] also called Gelfond's constant, [2] is the real number e raised to the power π. Its decimal expansion is given by: e π = 23.140 692 632 779 269 005 72... (sequence A039661 in the OEIS) Like both e and π, this constant is both irrational and transcendental.

  6. Pi - Wikipedia

    en.wikipedia.org/wiki/Pi

    The number π (/ p aɪ / ⓘ; spelled out as "pi") is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter.It appears in many formulae across mathematics and physics, and some of these formulae are commonly used for defining π, to avoid relying on the definition of the length of a curve.

  7. Leibniz formula for π - Wikipedia

    en.wikipedia.org/wiki/Leibniz_formula_for_π

    In mathematics, the Leibniz formula for π, named after Gottfried Wilhelm Leibniz, states that = + + = = +,. an alternating series.. It is sometimes called the Madhava–Leibniz series as it was first discovered by the Indian mathematician Madhava of Sangamagrama or his followers in the 14th–15th century (see Madhava series), [1] and was later independently rediscovered by James Gregory in ...

  8. Lindemann–Weierstrass theorem - Wikipedia

    en.wikipedia.org/wiki/Lindemann–Weierstrass...

    The theorem is also known variously as the Hermite–Lindemann theorem and the Hermite–Lindemann–Weierstrass theorem.Charles Hermite first proved the simpler theorem where the α i exponents are required to be rational integers and linear independence is only assured over the rational integers, [4] [5] a result sometimes referred to as Hermite's theorem. [6]

  9. List of formulae involving π - Wikipedia

    en.wikipedia.org/wiki/List_of_formulae_involving_π

    where C is the circumference of a circle, d is the diameter, and r is the radius.More generally, = where L and w are, respectively, the perimeter and the width of any curve of constant width.