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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 higher.
A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints. In geometry , a line segment is often denoted using an overline ( vinculum ) above the symbols for the two endpoints, such as in AB .
The needs of geometry, and also for example classical mechanics are to have a notion of curve in space of any number of dimensions. In general relativity, a world line is a curve in spacetime. If is a differentiable manifold, then we can define the notion of differentiable curve in . This general idea is enough to cover many of the applications ...
For example, a circle swept along a straight axis would define a cylinder (see Figure). A rectangle swept along a straight axis would define a "brick" (see Figure). Four dimensions with contrastive values (i.e., mutually exclusive values) define the current set of geons (see Figure): Shape of cross section: round vs. straight.
Visual Dictionary of Special Plane Curves; Curves and Surfaces Index (Harvey Mudd College) National Curve Bank; An elementary treatise on cubic and quartic curves by Alfred Barnard Basset (1901) online at Google Books
With these modern definitions, every geometric shape is defined as a set of points; this is not the case in synthetic geometry, where a line is another fundamental object that is not viewed as the set of the points through which it passes. However, there are modern geometries in which points are not primitive objects, or even without points.
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Line a is a great circle, the equivalent of a straight line in spherical geometry. Line c is equidistant to line a but is not a great circle. It is a parallel of latitude. Line b is another geodesic which intersects a in two antipodal points. They share two common perpendiculars (one shown in blue).