Minkowski's Question Mark Function

Minkowski's Question Mark Function

In mathematics, the Minkowski question mark function (or the slippery devil's staircase), denoted by ?(x), is a function possessing various unusual fractal properties, defined by Hermann Minkowski in 1904. It maps quadratic irrationals to rational numbers on the unit interval, via an expression relating the continued fraction expansions of the quadratics to the binary expansions of the rationals, given by Arnaud Denjoy in 1938. In addition, it maps rational numbers to dyadic rationals, as can be seen by a recursive definition closely related to the Stern–Brocot tree.

Read more about Minkowski's Question Mark Function:  Definition, Intuitive Explanation, Recursive Definition For Rational Arguments, Self-symmetry, Properties of ?(x), Conway Box Function, Historical References

Famous quotes containing the words question, mark and/or function:

    You may have your suspicions, your fears, you may even believe there is something, somewhere, terribly, drastically wrong, but because someone else is in charge, because there is a part of the system above you which you don’t know, you don’t question it, you even distrust your own doubts.
    Graham Swift (b. 1949)

    To do easily what is difficult for others is the mark of talent. To do what is impossible for talent is the mark of genius.
    Henri-Frédéric Amiel (1821–1881)

    Of all the inhabitants of the inferno, none but Lucifer knows that hell is hell, and the secret function of purgatory is to make of heaven an effective reality.
    Arnold Bennett (1867–1931)