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'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 ...
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 ...
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 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 .
In mathematics, a 3-manifold is a topological space that locally looks like a three-dimensional Euclidean space. A 3-manifold can be thought of as a possible shape of the universe. Just as a sphere looks like a plane (a tangent plane) to a small and close enough observer, all 3-manifolds look like our universe does to a small enough observer ...
A monkey's fist knot is essentially a 3-dimensional representation of the Borromean rings, albeit with three layers, in most cases. [41] Sculptor John Robinson has made artworks with three equilateral triangles made out of sheet metal, linked to form Borromean rings and resembling a three-dimensional version of the valknut.
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 ...
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