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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 ...
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 (,).
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.
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 ...
Move over, Wordle, Connections and Mini Crossword—there's a new NYT word game in town! The New York Times' recent game, "Strands," is becoming more and more popular as another daily activity ...
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].
Paulina Porizkova isn't going to sweat a little bit of weight gain.. The model, 59, shared on Instagram on Jan. 8 that she recently experienced some weight gain, and initially, it concerned her ...
A ferocious winter storm has brought historic snowfall amounts to the Midwest and is expected to pile up to a foot of snow in Washington D.C. The storm has broken daily snowfall records in ...