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Example of the use of descriptive geometry to find the shortest connector between two skew lines. The red, yellow and green highlights show distances which are the same for projections of point P. Given the X, Y and Z coordinates of P, R, S and U, projections 1 and 2 are drawn to scale on the X-Y and X-Z planes, respectively.
The plane has two dimensions because the length of a rectangle is independent of its width. In the technical language of linear algebra, the plane is two-dimensional because every point in the plane can be described by a linear combination of two independent vectors .
This familiar equation for a plane is called the general form of the equation of the plane or just the plane equation. [ 6 ] Thus for example a regression equation of the form y = d + ax + cz (with b = −1 ) establishes a best-fit plane in three-dimensional space when there are two explanatory variables.
In mathematics, a plane is a two-dimensional space or flat surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. When working exclusively in two-dimensional Euclidean space, the definite article is used, so the Euclidean plane refers to the ...
Let H = {h 1, h 2, ..., h k} be the convex hull of P; then the farthest-point Voronoi diagram is a subdivision of the plane into k cells, one for each point in H, with the property that a point q lies in the cell corresponding to a site h i if and only if d(q, h i) > d(q, p j) for each p j ∈ S with h i ≠ p j, where d(p, q) is the Euclidean ...
The most basic example is the flat Euclidean plane, an idealization of a flat surface in physical space such as a sheet of paper or a chalkboard. On the Euclidean plane, any two points can be joined by a unique straight line along which the distance can be measured.
Various scales may be used for different drawings in a set. For example, a floor plan may be drawn at 1:50 (1:48 or 1 ⁄ 4 ″ = 1′ 0″) whereas a detailed view may be drawn at 1:25 (1:24 or 1 ⁄ 2 ″ = 1′ 0″). Site plans are often drawn at 1:200 or 1:100. Scale is a nuanced subject in the use of engineering drawings.
A rotation in the plane can be formed by composing a pair of reflections. First reflect a point P to its image P′ on the other side of line L 1. Then reflect P′ to its image P′′ on the other side of line L 2. If lines L 1 and L 2 make an angle θ with one another, then points P and P′′ will make an angle 2θ around point O, the ...