Minkowski's Question Mark Function
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In mathematics, the Minkowski question mark function, sometimes called the slippery devil's staircase and 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.

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In mathematics, the Minkowski question mark function, sometimes called the slippery devil's staircase and 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.