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  2. 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.

  3. Cube root - Wikipedia

    en.wikipedia.org/wiki/Cube_root

    This means that in polar coordinates, we are taking the cube root of the radius and dividing the polar angle by three in order to define a cube root. With this definition, the principal cube root of a negative number is a complex number, and for instance 3 √ −8 will not be −2, but rather 1 + i √ 3.

  4. List of mathematical constants - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_constants

    1.41421 35623 73095 04880 [Mw 2] [OEIS 3] Positive root of = 1800 to 1600 BCE [5] Square root of 3, Theodorus' constant [6] 1.73205 08075 68877 29352 [Mw 3] [OEIS 4] Positive root of = 465 to 398 BCE Square root of 5 [7]

  5. Transcendental number - Wikipedia

    en.wikipedia.org/wiki/Transcendental_number

    For example, the square root of 2 is an irrational number, but it is not a transcendental number as it is a root of the polynomial equation x 2 − 2 = 0. The golden ratio (denoted φ {\displaystyle \varphi } or ϕ {\displaystyle \phi } ) is another irrational number that is not transcendental, as it is a root of the polynomial equation x 2 − ...

  6. Casus irreducibilis - Wikipedia

    en.wikipedia.org/wiki/Casus_irreducibilis

    Casus irreducibilis occurs when none of the roots are rational and when all three roots are distinct and real; the case of three distinct real roots occurs if and only if ⁠ q 2 / 4 ⁠ + ⁠ p 3 / 27 ⁠ < 0, in which case Cardano's formula involves first taking the square root of a negative number, which is imaginary, and then taking the ...

  7. Pi - Wikipedia

    en.wikipedia.org/wiki/Pi

    The number π (/ p aɪ /; spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159.The number π appears in many formulae across mathematics and physics.

  8. Nested radical - Wikipedia

    en.wikipedia.org/wiki/Nested_radical

    More generally, we find that + + + + is the positive real root of the equation x 3 − x − n = 0 for all n > 0. For n = 1, this root is the plastic ratio ρ, approximately equal to 1.3247. The same procedure also works to get as the real root of the equation x 3 + x − n = 0 for all n > 1.

  9. Ramanujan–Sato series - Wikipedia

    en.wikipedia.org/wiki/Ramanujan–Sato_series

    The first expansion is the McKay–Thompson series of class 1A (OEIS: A007240) with a(0) = 744. Note that, as first noticed by J. McKay , the coefficient of the linear term of j ( τ ) almost equals 196883, which is the degree of the smallest nontrivial irreducible representation of the monster group , a relationship called monstrous moonshine .