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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 ...
An oriented atlas on M is an atlas for which all transition functions are orientation preserving. M is orientable if it admits an oriented atlas. When n > 0, an orientation of M is a maximal oriented atlas. (When n = 0, an orientation of M is a function M → {±1}.) Orientability and orientations can also be expressed in terms of the tangent ...
Since in Green's theorem = (,) is a vector pointing tangential along the curve, and the curve C is the positively oriented (i.e. anticlockwise) curve along the boundary, an outward normal would be a vector which points 90° to the right of this; one choice would be (,).
Positive space refers to the areas of the work with a subject, while negative space is the space without a subject. [6] Open and closed space coincides with three-dimensional art, like sculptures, where open spaces are empty, and closed spaces contain physical sculptural elements.
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
The blue area above the x-axis may be specified as positive area, while the yellow area below the x-axis is the negative area. The integral of a real function can be imagined as the signed area between the -axis and the curve = over an interval [a, b].
The convention for positive linking number is based on a right-hand rule. The winding number of an oriented curve in the x-y plane is equal to its linking number with the z-axis (thinking of the z-axis as a closed curve in the 3-sphere). More generally, if either of the curves is simple, then the first homology group of its complement is ...