In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus...

In number theory, Dirichlet's theorem on Diophantine approximation, also called Dirichlet's approximation theorem, states that for any real numbers α {\displaystyle...

in Wiktionary, the free dictionary. Diophantine approximation Diophantine equation Diophantine quintuple Diophantine set This disambiguation page lists...

mathematician who won the Fields Medal for proving Roth's theorem on the Diophantine approximation of algebraic numbers. He was also a winner of the De Morgan Medal...

(3): 507–512. doi:10.1090/bull/1525. Waldschmidt, Michel (2013). Diophantine Approximation on Linear Algebraic Groups: Transcendence Properties of the Exponential...

instance how irrational numbers can be approximated by fractions (Diophantine approximation). Number theory is one of the oldest branches of mathematics alongside...

diophantine approximation to algebraic numbers. It is of a qualitative type, stating that algebraic numbers cannot have many rational approximations that...

formula for the volume of a dodecahedron. Hurwitz's theorem in Diophantine approximations states that every irrational number x can be approximated by infinitely...

The following lemma is usually known as Liouville's theorem (on diophantine approximation), there being several results known as Liouville's theorem. Lemma:...

achieved by approximation. Approximation theory is a branch of mathematics, and a quantitative part of functional analysis. Diophantine approximation deals...

calculations. They have also been used as auxiliary functions in Diophantine approximation and transcendental number theory, though for sharp results ad...

Littlewood conjecture is an open problem (as of April 2024[update]) in Diophantine approximation, proposed by John Edensor Littlewood around 1930. It states that...

show that π is approximately 3.14159. ⁠22/7⁠ is a widely used Diophantine approximation of π. It is a convergent in the simple continued fraction expansion...

In mathematics, a Diophantine equation is an equation, typically a polynomial equation in two or more unknowns with integer coefficients, for which only...

Kronecker's theorem is a theorem about diophantine approximation, introduced by Leopold Kronecker (1884). Kronecker's approximation theorem had been firstly proved...

groups, and the introduction of methods from ergodic theory into diophantine approximation. He was awarded a Fields Medal in 1978, a Wolf Prize in Mathematics...

Minkowski's question-mark function Minkowski space Work on the Diophantine approximations Spouse Auguste Adler Children 2 Scientific career Fields Mathematics...

90 MHz. Super PI version 1.9 is available from Super PI 1.9 page. Diophantine approximation Milü Madhava's correction term Pi is 3 Hayes, Brian (September...

mathematician, known for his work in number theory on Diophantine geometry and Diophantine approximation. In formulating Vojta's conjecture, he pointed out...

theorem on diophantine approximation. Bombieri & Gubler (2006) pp. 176–230. Bombieri, Enrico; Gubler, Walter (2006). Heights in Diophantine Geometry. New...

In number theory, specifically in Diophantine approximation theory, the Markov constant M ( α ) {\displaystyle M(\alpha )} of an irrational number α {\displaystyle...

The discrepancy can be bounded by the approximation exponent of α {\displaystyle \alpha } . If the approximation exponent is μ {\displaystyle \mu } , then...

the length of that subinterval. Such sequences are studied in Diophantine approximation theory and have applications to Monte Carlo integration. A sequence...

>1+{\frac {1}{n}}} . This result is due to Wolfgang M. Schmidt. Diophantine approximation Transcendental number Continued fraction Brjuno number Sondow...

things, his contributions to the Thue–Siegel–Roth theorem in Diophantine approximation, Siegel's method, Siegel's lemma and the Siegel mass formula for...

Davenport–Schmidt theorem (number theory, Diophantine approximations) Dirichlet's approximation theorem (Diophantine approximations) Dirichlet's theorem on arithmetic...

between diophantine approximation and Nevanlinna theory (value distribution theory) in complex analysis. It implies many other conjectures in Diophantine approximation...

unit circle, but with the power series truncated). The needs of Diophantine approximation are for auxiliary functions that are not generating functions—their...

curves. After a period when he worked on geometry of numbers and diophantine approximation, he returned in the later 1950s to the arithmetic of elliptic...

In mathematics, Diophantine geometry is the study of Diophantine equations by means of powerful methods in algebraic geometry. By the 20th century it became...