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For example, a circle of radius 2, centered at the origin of the plane, may be described as the set of all points whose coordinates x and y satisfy the equation x 2 + y 2 = 4; the area, the perimeter and the tangent line at any point can be computed from this equation by using integrals and derivatives, in a way that can be applied to any curve.
A point in the plane may be represented in homogeneous coordinates by a triple (x, y, z) where x/z and y/z are the Cartesian coordinates of the point. [10] This introduces an "extra" coordinate since only two are needed to specify a point on the plane, but this system is useful in that it represents any point on the projective plane without the ...
If in + + = the letters , and are taken as variables and , and are taken as constants then the equation becomes an equation of a set of lines in the space of all lines in the plane. Geometrically it represents the set of lines that pass through the point ( x , y , z ) {\displaystyle (x,y,z)} and may be interpreted as the equation of the point ...
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 ...
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. [9] Such a drawing is called a plane graph or planar embedding of the graph.
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Note that some words contain an ae which may not be written æ because the etymology is not from the Greek -αι-or Latin -ae-diphthongs. These include: In instances of aer (starting or within a word) when it makes the sound IPA [ɛə]/[eə] (air). Comes from the Latin āër, Greek ἀήρ. When ae makes the diphthong / eɪ / (lay) or / aɪ ...
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