About: Minkowski's question-mark function

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Minkowski's question-mark function Goto Sponge NotDistinct Permalink

An Entity of Type : owl:Thing, within Data Space : el.dbpedia.org associated with source document(s)

In mathematics, the Minkowski question-mark function, denoted by ?(x), is a function possessing various unusual fractal properties, defined by Hermann Minkowski in 1904. It maps quadratic irrational numbers 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.

Attributes	Values
rdfs:label	Minkowski's question-mark function (en)
rdfs:comment	In mathematics, the Minkowski question-mark function, denoted by ?(x), is a function possessing various unusual fractal properties, defined by Hermann Minkowski in 1904. It maps quadratic irrational numbers 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. (en)
dbp:wikiPageUsesTemplate	dbt:= dbt:Citation dbt:Cite_arXiv dbt:Math dbt:Mathworld dbt:More_footnotes dbt:Mvar dbt:Reflist dbt:Sfnp dbt:Sfrac dbt:Sqrt dbt:Use_dmy_dates dbt:Wide_image dbt:Abs dbt:Closed-closed
Subject	Articles with example C code Continued fractions Continuous mappings De Rham curves Special functions Hermann Minkowski
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Minkowski's_question-mark_function?oldid=1069784630&ns=0
Wikipage page ID	1475109 (xsd:integer)
page length (characters) of wiki page	27325 (xsd:nonNegativeInteger)
Wikipage revision ID	1069784630 (xsd:integer)
Link from a Wikipage to another Wikipage	Fractal Unimodular matrix Unit interval West Virginia University Absolute continuity Algebraic number Algorithm Almost everywhere Arnaud Denjoy Binary number Monoid Monotonic function Self-similarity University of Nottingham C (programming language) Cambridge Cambridge University Press Cantor's isomorphism theorem Cantor function Articles with example C code Continued fractions Continuous mappings De Rham curves Special functions Boltzmann distribution Hermann Minkowski Division by two Quadratic irrational number Cumulative distribution function De Rham curve Linear fractional transformation Run-length encoding Springer Science+Business Media Ternary numeral system Concatenation Continued fraction Dyadic rational Dyadic transformation Hermann Minkowski Order isomorphism Fixed-point subgroup Function (mathematics) Composition operator Graph of a function Periodic continued fraction Periodic function Periodic point Derivative Determinant Farey sequence Irrational number Irreducible fraction Modular group Transactions of the American Mathematical Society Transcendental number Even and odd functions Stern–Brocot tree Loop invariant Loop variant Mathematics Mathematische Annalen Measure (mathematics) Multifractal system Point reflection Pompeiu derivative Raphaël Salem Rational number Recursion Singular distribution
has abstract	In mathematics, the Minkowski question-mark function, denoted by ?(x), is a function possessing various unusual fractal properties, defined by Hermann Minkowski in 1904. It maps quadratic irrational numbers 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. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Minkowski's_question-mark_function

Faceted Search & Find service v1.17_git151 as of Feb 20 2025

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 07.20.3240 as of Nov 11 2024, on Linux (x86_64-ubuntu_focal-linux-gnu), Single-Server Edition (72 GB total memory, 1 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2025 OpenLink Software