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Line 1: − + − − Attempts at providing a rigorous, abstract definition usually face philosophical [[paradox]]es, such as [[Euclid]]'s contention that lines are objects with "breadthless length." In other words, he asserted that a line in infinitely long, but has no width. Lines can also be considered as points strung together, or as curves with infinite [[radius]] of [[curvature]], yet both these definitions have philosophical flaws as well. − − A line that can be drawn on paper is not actually a line, but a representation of a line. Two points determine a line. A line can be broken down into finite [[line segment]]s. − − Common mathematical representations of a line include: − − In 2 dimensions in the [[Cartesian plane]]: − *Standard Form: ax + by + c = 0 − *Slope-Intercept Form: y = mx + b (where m is the [[slope]] of the line, b is the [[y-intercept]]) − *Point-Slope Form: (y - y<sub>0</sub>) = m(x - x<sub>0</sub>) (where m is the slope and (x<sub>0</sub>, y<sub>0</sub>) is a point on the line) − − In n dimensions in [[Cartesian coordinates]]: − *Parametrized Vector Form: r(t) = <x<sub>0</sub>, y<sub>0</sub>,...> + t<x, y,...>
remove blather - what we need is a basic, workable definition
The '''line''' is a basic [[geometry|geometric]] [[shape]]. It is such an intuitive concept that most mathematicians think it escapes a formal, general definition. Other such intuitive concepts are the [[point]], the [[plane]], the [[set]], [[symmetry]], and [[infinity]].
The '''line''' is a basic [[geometry|geometric]] [[shape]].
[[Category:Geometry]]
[[Category:Geometry]]