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Plane_Crazy_(SILENT).webm (WebM audio/video file, VP9, length 6 min 0 s, 640 × 480 pixels, 1.9 Mbps overall, file size: 81.64 MB) This is a file from the Wikimedia Commons . Information from its description page there is shown below.
There are two ways to formally define affine planes, which are equivalent for affine planes over a field. The first way consists in defining an affine plane as a set on which a vector space of dimension two acts simply transitively. Intuitively, this means that an affine plane is a vector space of dimension two in which one has "forgotten ...
Optical flow or optic flow is the pattern of apparent motion of objects, surfaces, and edges in a visual scene caused by the relative motion between an observer and a scene. [ 1 ] [ 2 ] Optical flow can also be defined as the distribution of apparent velocities of movement of brightness pattern in an image.
A similar construction, starting from the projective plane of order 3, produces the affine plane of order 3 sometimes called the Hesse configuration. An affine plane of order n exists if and only if a projective plane of order n exists (however, the definition of order in these two cases is not the same). Thus, there is no affine plane of order ...
To define the special affine curvature, it is necessary first to define the special affine arclength (also called the equiaffine arclength). Consider an affine plane curve β(t). Choose coordinates for the affine plane such that the area of the parallelogram spanned by two vectors a = (a 1, a 2) and b = (b 1, b 2) is given by the determinant
A plane is said to have the "minor affine Desargues property" when two triangles in parallel perspective, having two parallel sides, must also have the third sides parallel. If this property holds in the affine plane defined by a ternary ring, then there is an equivalence relation between "vectors" defined by pairs of points from the plane. [14]
In mathematics, the affine group or general affine group of any affine space is the group of all invertible affine transformations from the space into itself. In the case of a Euclidean space (where the associated field of scalars is the real numbers), the affine group consists of those functions from the space to itself such that the image of every line is a line.
In geometry, a hyperplane of an n-dimensional space V is a subspace of dimension n − 1, or equivalently, of codimension 1 in V.The space V may be a Euclidean space or more generally an affine space, or a vector space or a projective space, and the notion of hyperplane varies correspondingly since the definition of subspace differs in these settings; in all cases however, any hyperplane can ...