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    Pi

    Decimal approximation

    3.1415926535897932384626433832795028841971693993751058209749445923...

    Property

    π is a transcendental number

    Number line

    Number line

    Continued fraction

    [3; 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, 84, 2, 1, 1, 15, 3, 13, ...]

    Alternative representations

    π = 180 °

    π = -i log(-1)

    π = cos^(-1)(-1)

    Series representations

    π = 4 sum_(k=0)^∞ (-1)^k/(2 k + 1)

    π = -2 + 2 sum_(k=1)^∞ 2^k/binomial(2 k, k)

    π = sum_(k=0)^∞ (50 k - 6)/(2^k binomial(3 k, k))

    Integral representations

    π = 2 integral_0^∞ 1/(t^2 + 1) dt

    π = 4 integral_0^1 sqrt(1 - t^2)dt

    π = 2 integral_0^∞ sin(t)/t dt

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