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In 2-dimensional space, there is a line/axis of symmetry, in 3-dimensional space, there is a plane of symmetry. An object or figure which is indistinguishable from its transformed image is called mirror symmetric. In conclusion, a line of symmetry splits the shape in half and those halves should be identical.
The four quadrants of a Cartesian coordinate system. The axes of a two-dimensional Cartesian system divide the plane into four infinite regions, called quadrants, each bounded by two half-axes.
Each axis is usually named after the coordinate which is measured along it; so one says the x-axis, the y-axis, the t-axis, etc. Another common convention for coordinate naming is to use subscripts, as (x 1, x 2, ..., x n) for the n coordinates in an n-dimensional space, especially when n is greater than 3 or unspecified.
Along a vertical axis (often the y-axis): The top and bottom views, which are known as plans (because they show the arrangement of features on a horizontal plane, such as a floor in a building). Along a horizontal axis (often the z -axis): The front and back views, which are known as elevations (because they show the heights of features of an ...
A curve is a 1-dimensional object that may be straight (like a line) or not; curves in 2-dimensional space are called plane curves and those in 3-dimensional space are called space curves. [52] In topology, a curve is defined by a function from an interval of the real numbers to another space. [49]
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 ...
Rational Bézier curve – polynomial curve defined in homogeneous coordinates (blue) and its projection on plane – rational curve (red) In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcul, [1] [2] [3] are a system of coordinates used in projective geometry, just as Cartesian coordinates are used ...
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