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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 ...
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 .
For n > 3, the result is a 3-dimensional bulb-like structure with fractal surface detail and a number of "lobes" depending on n. Many of their graphic renderings use n = 8. However, the equations can be simplified into rational polynomials when n is odd. For example, in the case n = 3, the third power can be simplified into the more elegant form:
'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 ...
Example of line art (published in The Survey, October 1917–March 1918). Line art or line drawing is any image that consists of distinct straight lines or curved lines placed against a background (usually plain). Two-dimensional or three-dimensional objects are often represented through shade (darkness) or hue . Line art can use lines of ...
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. In drawing or painting, space is not actually there, but the illusion of it is.
A form is an artist's way of using elements of art, principles of design, and media. Form, as an element of art, is three-dimensional and encloses space. Like a shape, a form has length and width, but it also has depth. Forms are either geometric or free-form, and can be symmetrical or asymmetrical.
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.