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- Hilbert's_seventh_problem abstract "Hilbert's seventh problem is one of David Hilbert's list of open mathematical problems posed in 1900. It concerns the irrationality and transcendence of certain numbers (Irrationalität und Transzendenz bestimmter Zahlen). Two specific questions are asked:In an isosceles triangle, if the ratio of the base angle to the angle at the vertex is algebraic but not rational, is then the ratio between base and side always transcendental?Is always transcendental, for algebraic and irrational algebraic ? The second question was answered in the affirmative by Aleksandr Gelfond in 1934, and refined by Theodor Schneider in 1935. This result is known as Gelfond's theorem or the Gelfond–Schneider theorem. (The restriction to irrational b is important, since it is easy to see that is algebraic for algebraic a and rational b.)From the point of view of generalisations, this is the case of the general linear form in logarithms which was attacked by Gelfond and then solved by Alan Baker. It is called the Gelfond conjecture or Baker's theorem. Baker was rewardedas a Fields Medal winner in 1970 because of this.The first question is a consequence of the second question.".
- Hilbert's_seventh_problem wikiPageExternalLink prob7.
- Hilbert's_seventh_problem wikiPageID "392579".
- Hilbert's_seventh_problem wikiPageRevisionID "596199805".
- Hilbert's_seventh_problem hasPhotoCollection Hilbert's_seventh_problem.
- Hilbert's_seventh_problem subject Category:Hilbert's_problems.
- Hilbert's_seventh_problem type Abstraction100002137.
- Hilbert's_seventh_problem type Attribute100024264.
- Hilbert's_seventh_problem type Condition113920835.
- Hilbert's_seventh_problem type Difficulty114408086.
- Hilbert's_seventh_problem type Hilbert'sProblems.
- Hilbert's_seventh_problem type Problem114410605.
- Hilbert's_seventh_problem type State100024720.
- Hilbert's_seventh_problem comment "Hilbert's seventh problem is one of David Hilbert's list of open mathematical problems posed in 1900. It concerns the irrationality and transcendence of certain numbers (Irrationalität und Transzendenz bestimmter Zahlen).".
- Hilbert's_seventh_problem label "Hilbert's seventh problem".
- Hilbert's_seventh_problem label "Septième problème de Hilbert".
- Hilbert's_seventh_problem label "Settimo problema di Hilbert".
- Hilbert's_seventh_problem label "Sétimo problema de Hilbert".
- Hilbert's_seventh_problem label "Седьмая проблема Гильберта".
- Hilbert's_seventh_problem label "معضلة هيلبرت السابعة".
- Hilbert's_seventh_problem label "希爾伯特第七問題".
- Hilbert's_seventh_problem sameAs Septième_problème_de_Hilbert.
- Hilbert's_seventh_problem sameAs Settimo_problema_di_Hilbert.
- Hilbert's_seventh_problem sameAs Sétimo_problema_de_Hilbert.
- Hilbert's_seventh_problem sameAs m.022wpg.
- Hilbert's_seventh_problem sameAs Q2584447.
- Hilbert's_seventh_problem sameAs Q2584447.
- Hilbert's_seventh_problem sameAs Hilbert's_seventh_problem.
- Hilbert's_seventh_problem wasDerivedFrom Hilbert's_seventh_problem?oldid=596199805.
- Hilbert's_seventh_problem isPrimaryTopicOf Hilbert's_seventh_problem.