skew lines

Take for example a set of 2n points in R all lying on two skew lines.

A few people have trouble negotiating stairs that have skewed lines as reference points.

Let d be the distance between the skew lines formed by opposite edges a and b c as calculated here.

As they exist now, the two world championships are like the skew lines in solid geometry: they will never meet.

Skew lines are straight lines that are neither parallel nor intersecting.

A plane equidistant from two skew lines in general positions (say, to confirm safe radiation distance?)

Similarly, in 3D space a very small perturbation of two parallel or intersecting lines will almost certainly turn them into skew lines.

In this sense, skew lines are the "usual" case, and parallel or intersecting lines are special cases.

Any three skew lines in R lie on exactly one ruled surface of one of these types .

The hyperbolic paraboloid is a doubly ruled surface: it contains two families of mutually skew lines.

A configuration of skew lines is a set of lines in which all pairs are skew.

In solid geometry, skew lines are two lines that do not intersect and are not parallel.

Two skew lines (pipes, perhaps) in general positions in order to determine the location of their shortest connector (common perpendicular)

For example: To find the general solution such that two, unequal length, skew lines in general positions (say, rockets in flight?)

Lines that are coplanar either intersect or are parallel, so skew lines exist only in three or more dimensions.

In particular, when and move with constant speed along two skew lines, the surface is a hyperbolic paraboloid, or a piece of an hyperboloid of one sheet.

A simple example of a pair of skew lines is the pair of lines through opposite edges of a regular tetrahedron.

Similarly, in three or more dimensions, even two lines almost certainly do not intersect; pairs of lines that do not intersect are called skew lines.

This formula supplies an easy method to find the angle between two planes (or curved surfaces) from their normal vectors and between skew lines from their vector equations.

Cleverly skewed lines and planes and angles act to pull the eye in, although - unless you're in the building across the street - the neck must be craned for an optimum view.

Image:Descriptive geometry - skew lines appearing perpendicular.png 'Figure 1: Descriptive geometry - skew lines appearing perpendicular'

This is true if the ambient space is two-dimensional, but false if the ambient space is three-dimensional, because in the latter case the lines could be skew lines, rather than parallel.

Like the hyperboloid of one sheet, the hyperbolic paraboloid has two families of skew lines; in each of the two families the lines are parallel to a common plane although not to each other.

Any two opposite edges of a tetrahedron lie on two skew lines, and the distance between the edges is defined as the distance between the two skew lines.

Any two skew lines of these 27 belong to a unique Schläfli double six configuration, a set of 12 lines whose intersection graph is a crown graph in which the two lines have disjoint neighborhoods.