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In mathematics, the Reeb foliation is a particular foliation of the 3-sphere, introduced by the French mathematician Georges Reeb (1920–1993). It is based on dividing the sphere into two solid tori , along a 2- torus : see Clifford torus .
2-dimensional section of Reeb foliation 3-dimensional model of Reeb foliation. In mathematics (differential geometry), a foliation is an equivalence relation on an n-manifold, the equivalence classes being connected, injectively immersed submanifolds, all of the same dimension p, modeled on the decomposition of the real coordinate space R n into the cosets x + R p of the standardly embedded ...
'Trefoil' is a term in Gothic architecture given to the ornamental foliation or cusping introduced in the heads of window-lights, tracery, and panellings, in which the centre takes the form of a three-lobed leaf (formed from three partially overlapping circles). One of the earliest examples is in the plate tracery at Winchester Cathedral (1222 ...
The leaf is a torus T 2 bounding a solid torus with the Reeb foliation. The theorem was proved by Sergei Novikov in 1964. Earlier, Charles Ehresmann had conjectured that every smooth codimension-one foliation on S 3 had a compact leaf, which was known to be true for all known examples; in particular, the Reeb foliation has a compact leaf that ...
Intersection lineations are measured in relation to the two structures which intersect to form them. For instance, according to the measurement conventions of structural geology, original bedding, S 0 intersected by a fold's axial plane foliation, forms an intersection lineation L 0-1, with an azimuth and
The Froebel gifts (German: Fröbelgaben) are educational play materials for young children, originally designed by Friedrich Fröbel for the first kindergarten at Bad Blankenburg. Playing with Froebel gifts, singing, dancing, and growing plants were each important aspects of this child-centered approach to education.
Hyperbolic geometry is the most rich and least understood of the eight geometries in dimension 3 (for example, for all other geometries it is not hard to give an explicit enumeration of the finite-volume manifolds with this geometry, while this is far from being the case for hyperbolic manifolds). After the proof of the Geometrisation ...
In the visual arts, shape is a flat, enclosed area of an artwork created through lines, textures, or colours, or an area enclosed by other shapes, such as triangles, circles, and squares. [1] Likewise, a form can refer to a three-dimensional composition or object within a three-dimensional composition. [2]