Difference between revisions of "Line"
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| − | A line was described by [[Euclid]] as having "breadthless length. This means that a line in infinitely long, but has no width. 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. | + | A line was described by [[Euclid]] as having "breadthless length. This means that a line in infinitely long, but has no width. Lines can be considered as curves with infinite radius of curvature. 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: | ||
| + | *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 - y0) = m(x - x0) (where m is the slope and (x0, y0) is a point on the line) | ||
| + | |||
| + | In n dimensions: | ||
| + | *Parametrized Vector Form: r(t) = <x0, y0,...> + t<x, y,...> | ||
[[Category:Geometry]] | [[Category:Geometry]] | ||
Revision as of 17:23, March 17, 2007
A line was described by Euclid as having "breadthless length. This means that a line in infinitely long, but has no width. Lines can be considered as curves with infinite radius of curvature. 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 Segments.
Common mathematical representations of a line include:
In 2 dimensions:
- 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 - y0) = m(x - x0) (where m is the slope and (x0, y0) is a point on the line)
In n dimensions:
- Parametrized Vector Form: r(t) = <x0, y0,...> + t<x, y,...>