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In geometry, a straight line, usually abbreviated line, is an infinitely long object with no width, depth, or curvature, an idealization of such physical objects as a straightedge, a taut string, or a ray of light. Lines are spaces of dimension one, which may be embedded in spaces of dimension two, three, or
Coordinate charts are mathematical objects of topological manifolds, and they have multiple applications in theoretical and applied mathematics. When a differentiable structure and a metric are defined, greater structure exists, and this allows the definition of constructs such as integration and geodesics .
A linear equation in line coordinates has the form al + bm + c = 0, where a, b and c are constants. Suppose (l, m) is a line that satisfies this equation.If c is not 0 then lx + my + 1 = 0, where x = a/c and y = b/c, so every line satisfying the original equation passes through the point (x, y).
In geometry, an arrangement of lines is the subdivision of the Euclidean plane formed by a finite set of lines. An arrangement consists of bounded and unbounded convex polygons , the cells of the arrangement, line segments and rays , the edges of the arrangement, and points where two or more lines cross, the vertices of the arrangement.
In combinatorial mathematics, a Levi graph or incidence graph is a bipartite graph associated with an incidence structure. [1] [2] From a collection of points and lines in an incidence geometry or a projective configuration, we form a graph with one vertex per point, one vertex per line, and an edge for every incidence between a point and a line.
GeoGebra is a dynamic geometry program that can be used to create geometric objects free-hand using compass-and-ruler tools. It can also be used to plot implicit curves, parametric curves, and loci of points. It supports SVG, PNG, EPS, PDF, EMF, PGF/TikZ and PSTricks as export formats and has support for LaTeX formulas within text objects.
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