Poincaré
Encyclopedia
Several members of the French Poincaré family have been successful in public and scientific life:
In physics and mathematics, a number of ideas are named after Henri Poincaré:
- Henri PoincaréHenri PoincaréJules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...
(1854–1912), physicist, mathematician and philosopher of science - Lucien PoincaréLucien Poincaré-Biography:Poincaré was born at Bar-le-Duc July 22, 1862. After a distinguished academic career he became in succession inspector general of physical science in 1902, director of secondary education at the Ministry of Public Instruction in 1910, director of higher education in 1914 and rector of...
(1862–1920), physicist, brother of Raymond and cousin of Henri - Raymond PoincaréRaymond PoincaréRaymond Poincaré was a French statesman who served as Prime Minister of France on five separate occasions and as President of France from 1913 to 1920. Poincaré was a conservative leader primarily committed to political and social stability...
(1860–1934), statesman, cousin of Henri
In physics and mathematics, a number of ideas are named after Henri Poincaré:
- Poincaré conjecturePoincaré conjectureIn mathematics, the Poincaré conjecture is a theorem about the characterization of the three-dimensional sphere , which is the hypersphere that bounds the unit ball in four-dimensional space...
- Poincaré recurrence
- Poincaré groupPoincaré groupIn physics and mathematics, the Poincaré group, named after Henri Poincaré, is the group of isometries of Minkowski spacetime.-Simple explanation:...
, the group of isometries of Minkowski spacetime, named in honour of Henri Poincaré - Poincaré inequalityPoincaré inequalityIn mathematics, the Poincaré inequality is a result in the theory of Sobolev spaces, named after the French mathematician Henri Poincaré. The inequality allows one to obtain bounds on a function using bounds on its derivatives and the geometry of its domain of definition. Such bounds are of great...
- Poincaré mapPoincaré mapIn mathematics, particularly in dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is the intersection of a periodic orbit in the state space of a continuous dynamical system with a certain lower dimensional subspace, called the Poincaré section, transversal to...
- Poincaré modelPoincaré modelPoincaré model can refer to:*Poincaré disk model, a model of n-dimensional hyperbolic geometry*Poincaré half-plane model, a model of two-dimensional hyperbolic geometry...
of non-Euclidean geometry - Poincaré–Hopf theoremPoincaré–Hopf theoremIn mathematics, the Poincaré–Hopf theorem is an important theorem that is still used today in differential topology...
- Poincaré dualityPoincaré dualityIn mathematics, the Poincaré duality theorem named after Henri Poincaré, is a basic result on the structure of the homology and cohomology groups of manifolds...
- Poincaré–Birkhoff–Witt theoremPoincaré–Birkhoff–Witt theoremIn the theory of Lie algebras, the Poincaré–Birkhoff–Witt theorem is a result giving an explicit description of the universal enveloping algebra of a Lie algebra...
- Hilbert–Poincaré seriesHilbert–Poincaré seriesIn mathematics, and in particular in the field of algebra, a Hilbert–Poincaré series , named after David Hilbert and Henri Poincaré, is an adaptation of the notion of dimension to the context of graded algebraic structures...
- Poincaré metricPoincaré metricIn mathematics, the Poincaré metric, named after Henri Poincaré, is the metric tensor describing a two-dimensional surface of constant negative curvature. It is the natural metric commonly used in a variety of calculations in hyperbolic geometry or Riemann surfaces.There are three equivalent...
- Poincaré half-plane modelPoincaré half-plane modelIn non-Euclidean geometry, the Poincaré half-plane model is the upper half-plane , together with a metric, the Poincaré metric, that makes it a model of two-dimensional hyperbolic geometry....
- Poincaré–Lindstedt method