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This definition relies on the fact that every simple closed curve admits a well-defined interior, which follows from the Jordan curve theorem. The inner loop of a beltway road in a country where people drive on the right side of the road is an example of a negatively oriented ( clockwise ) curve.
The orientation of a real vector space or simply orientation of a vector space is the arbitrary choice of which ordered bases are "positively" oriented and which are "negatively" oriented. In the three-dimensional Euclidean space , right-handed bases are typically declared to be positively oriented, but the choice is arbitrary, as they may also ...
Lemma 1 (Decomposition Lemma) — Assume is a rectifiable, positively oriented Jordan curve in the plane and let be its inner region. For every positive real δ {\displaystyle \delta } , let F ( δ ) {\displaystyle {\mathcal {F}}(\delta )} denote the collection of squares in the plane bounded by the lines x = m δ , y = m δ {\displaystyle x=m ...
Serpentine lines from Hogarth's The Analysis of Beauty. Line of beauty is a term and a theory in art or aesthetics used to describe an S-shaped curved line (a serpentine line) appearing within an object, as the boundary line of an object, or as a virtual boundary line formed by the composition of several objects.
An example of a 1-dimensional manifold is an interval [a, b], and intervals can be given an orientation: they are positively oriented if a < b, and negatively oriented otherwise. If a < b then the integral of the differential 1 -form f ( x ) dx over the interval [ a , b ] (with its natural positive orientation) is
Mark making is the interaction between the artist and the materials they are using. [1] It provides the viewer of the work with an image of what the artist had done to create the mark, reliving what the artist had done at the time. [1] Materiality is the choice of materials used and how it impacts the work of art and how the viewer perceives it ...
Why the Pawtucket S curve exists on I-95. When the government was gearing up to build the interstate highway system in the 1950s, the main concern many people had was whether their land would be ...
Let C be a positively oriented, piecewise smooth, simple closed curve in a plane, and let D be the region bounded by C. If L and M are functions of ( x , y ) defined on an open region containing D and have continuous partial derivatives there, then [ 7 ] [ 8 ]