Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Basel_problem> ?p ?o. }
Showing items 1 to 47 of
47
with 100 items per page.
- Basel_problem abstract "The Basel problem is a famous problem in mathematical analysis with relevance to number theory, first posed by Pietro Mengoli in 1644 and solved by Leonhard Euler in 1735. Since the problem had withstood the attacks of the leading mathematicians of the day, Euler's solution brought him immediate fame when he was twenty-eight. Euler generalised the problem considerably, and his ideas were taken up years later by Bernhard Riemann in his seminal 1859 paper On the Number of Primes Less Than a Given Magnitude, in which he defined his zeta function and proved its basic properties. The problem is named after Basel, hometown of Euler as well as of the Bernoulli family who unsuccessfully attacked the problem.The Basel problem asks for the precise summation of the reciprocals of the squares of the natural numbers, i.e. the precise sum of the infinite series:The series is approximately equal to 1.644934 OEIS A013661. The Basel problem asks for the exact sum of this series (in closed form), as well as a proof that this sum is correct. Euler found the exact sum to be π2/6 and announced this discovery in 1735. His arguments were based on manipulations that were not justified at the time, and it was not until 1741 that he was able to produce a truly rigorous proof.".
- Basel_problem wikiPageExternalLink infinite-series-surprises.
- Basel_problem wikiPageExternalLink zeta2.pdf.
- Basel_problem wikiPageExternalLink How%20Euler%20Did%20It%2002%20Estimating%20the%20Basel%20Problem.pdf.
- Basel_problem wikiPageExternalLink E352.pdf.
- Basel_problem wikiPageExternalLink p25.pdf.
- Basel_problem wikiPageID "490303".
- Basel_problem wikiPageRevisionID "601688885".
- Basel_problem hasPhotoCollection Basel_problem.
- Basel_problem subject Category:Articles_containing_proofs.
- Basel_problem subject Category:Mathematical_problems.
- Basel_problem subject Category:Number_theory.
- Basel_problem subject Category:Zeta_and_L-functions.
- Basel_problem type Abstraction100002137.
- Basel_problem type Attribute100024264.
- Basel_problem type Condition113920835.
- Basel_problem type Difficulty114408086.
- Basel_problem type MathematicalProblems.
- Basel_problem type Problem114410605.
- Basel_problem type State100024720.
- Basel_problem comment "The Basel problem is a famous problem in mathematical analysis with relevance to number theory, first posed by Pietro Mengoli in 1644 and solved by Leonhard Euler in 1735. Since the problem had withstood the attacks of the leading mathematicians of the day, Euler's solution brought him immediate fame when he was twenty-eight.".
- Basel_problem label "Basel problem".
- Basel_problem label "Basler Problem".
- Basel_problem label "Bazel-probleem".
- Basel_problem label "Problem bazylejski".
- Basel_problem label "Problema de Basilea".
- Basel_problem label "Problema de Basileia".
- Basel_problem label "Problema di Basilea".
- Basel_problem label "Problème de Bâle".
- Basel_problem label "معضلة بازل".
- Basel_problem label "バーゼル問題".
- Basel_problem label "巴塞尔问题".
- Basel_problem sameAs Basler_Problem.
- Basel_problem sameAs Problema_de_Basilea.
- Basel_problem sameAs Problème_de_Bâle.
- Basel_problem sameAs Problema_di_Basilea.
- Basel_problem sameAs バーゼル問題.
- Basel_problem sameAs 바젤_문제.
- Basel_problem sameAs Bazel-probleem.
- Basel_problem sameAs Problem_bazylejski.
- Basel_problem sameAs Problema_de_Basileia.
- Basel_problem sameAs m.02gr60.
- Basel_problem sameAs Q810431.
- Basel_problem sameAs Q810431.
- Basel_problem sameAs Basel_problem.
- Basel_problem wasDerivedFrom Basel_problem?oldid=601688885.
- Basel_problem isPrimaryTopicOf Basel_problem.