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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 ...
Intersection lineations are linear structures formed by the intersection of any two surfaces in a three-dimensional space. The trace of bedding on an intersecting foliation plane commonly appears as colour stripes generally parallel to local fold's hinges. Intersection lineations can also be due to the intersection of two foliations.
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 .
'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 ...
In other words, every point admits a foliation chart, i.e. the distribution is tangent to the leaves of a foliation. Moreover, this local characterisation coincides with the definition of integrability for a G {\displaystyle G} -structures , when G {\displaystyle G} is the group of real invertible upper-triangular block matrices (with ( n × n ...
Foliation in geology refers to repetitive layering in metamorphic rocks. [1] Each layer can be as thin as a sheet of paper, or over a meter in thickness. [ 1 ] The word comes from the Latin folium , meaning "leaf", and refers to the sheet-like planar structure. [ 1 ]
Multifoil arch in the Aljafería, Zaragoza, Spain. A multifoil arch (or polyfoil arch), also known as a cusped arch, [1] [2] polylobed arch, [3] [4] or scalloped arch, [5] is an arch characterized by multiple circular arcs or leaf shapes (called foils, lobes, or cusps) that are cut into its interior profile or intrados.
Space is the area around, above, and within an object. Photographers can capture space, architects build space, and painters create space. This element is found in each of the visual arts. It can be positive or negative, open or closed, shallow or deep, and two-dimensional or three-dimensional.