Poincaré in a sentence

Gauss and Poincaré Carl Friedrich Gauss Henri Poincaré Although there was a prevailing Kantian consensus at the time, once non-Euclidean geometries had been formalised, some began to wonder whether or not physical space is curved.

Henri Poincaré citation In it, he discussed Poincaré's regular schedule: * He worked during the same times each day in short periods of time.

Poincaré never declared whether he believed this additional condition would characterize the 3-sphere, but nonetheless, the statement that it does is known as the Poincaré conjecture.

Poincaré proved a formula relating the number of edges, vertices and faces of n-dimensional polyhedron (the Euler–Poincaré theorem) and gave the first precise formulation of the intuitive notion of dimension.

The set of Poincaré transformations also satisfy the properties of a group and is called the Poincaré group or inhomogeneous Lorentz group.

Whittaker 1953, Secondary sources on relativity Character Photographic portrait of H. Poincaré by Henri Manuel Poincaré's work habits have been compared to a bee flying from flower to flower.

Aleksandr Lyapunov and Jules Henri Poincaré worked on the foundations of chaos theory without any computer at all.

Any two antipodal points on the Poincaré sphere refer to orthogonal polarization states.

A Report on the Poincaré Conjecture.

At the same time, Poincaré was preparing for his doctorate in sciences in mathematics under the supervision of Charles Hermite.

But the foundation of this science, for a space of any dimension, was created by Poincaré.

But today, the Poincaré conjecture has been proven using time as a mathematical concept in which objects can flow (see Ricci flow ).

Chaos theory and the sensitive dependence on initial conditions were described in the literature in a particular case of the three-body problem by Henri Poincaré in 1890.

Conventionalism The French mathematician Henri Poincaré was among the first to articulate a conventionalist view.

Couturat, said Poincaré, had accepted the Peano axioms as a definition of a number.

Earlier in his career, Smale was involved in controversy over remarks he made regarding his work habits while proving the higher-dimensional Poincaré conjecture.

For a given power in the polarized component given by: : the set of all polarization states are then mapped to points on the surface of the so-called Poincaré sphere (but of radius P), as shown in the accompanying diagram.

For dimensions greater than three, one can pose the Generalized Poincaré conjecture: is a homotopy n-sphere homeomorphic to the n-sphere?

From a fundamental physics perspective, mass is the number describing under which the representation of the little group of the Poincaré group a particle transforms.

Generalizing a theory of Bruns (1887), Poincaré showed that the three-body problem is not integrable.