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Explanation, Recursive Definition For Rational Arguments, Self-symmetry, Properties of ?(x), Conway Box Function, Historical References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:
“Truth cannot be defined or tested by agreement with ‘the world’; for not only do truths differ for different worlds but the nature of agreement between a world apart from it is notoriously nebulous. Rather—speaking loosely and without trying to answer either Pilate’s question or Tarski’s—a version is to be taken to be true when it offends no unyielding beliefs and none of its own precepts.”
—Nelson Goodman (b. 1906)
“It is easier for a camel to go through the eye of a needle than for someone who is rich to enter the kingdom of God.”
—Bible: New Testament, Mark 10:25.
Jesus.
“The art of living is to function in society without doing violence to one’s own needs or to the needs of others. The art of mothering is to teach the art of living to children.”
—Elaine Heffner (20th century)