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Explanation, Recursive Definition For Rational Arguments, Self-symmetry, Properties of ?(x), Conway Box Function, Historical References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:
“The moment the doctrine of the immortality is separately taught, man is already fallen. In the flowing of love, in the adoration of humility, there is no question of continuance. No inspired man ever asks this question, or condescends to these evidences. For the soul is true to itself, and the man in whom it is shed abroad cannot wander from the present, which is infinite, to a future which would be finite.”
—Ralph Waldo Emerson (1803–1882)
“Both magic and religion are based strictly on mythological tradition, and they also both exist in the atmosphere of the miraculous, in a constant revelation of their wonder-working power. They both are surrounded by taboos and observances which mark off their acts from those of the profane world.”
—Bronislaw Malinowski (1884–1942)
“My function in life is not to be a politician in Parliament: it is to get something done.”
—Bernadette Devlin (b. 1947)