Line (geometry)#Ray

The beam and the half-line in geometry - clearly spoken - a straight line that is bounded on one side, but extends to the other side to infinity.

• The half-line is a geometric object, which occurs when a point is a straight line on which it lies, is divided. Here, the point is either part of the half-line or not.
• The beam has an orientation: It starts from an initial point.

Rays and half-lines must therefore be distinguished from straight lines on both sides unlimited, and of routes which are bounded on both sides.

Geometric representation

The notation used in the diagram [AB expresses that there is a subset of the line AB, which is defined by point A, but extends beyond the point B also.

With the help of intermediate relation ( " ... is between ... and ..." ) can be the half-line [AB defined as the set of all points X on the line AB, is for the A not between B and X.

Consider a line g and an arbitrary point P on g, so these are the two defined thereby rays ( half-lines ) s1 and s2 are characterized as non-empty subsets of g that satisfy the following conditions:

• Each point on the straight line G, which does not coincide with P belongs to exactly one of the two subsets S1 or S2.
• P1 is an arbitrary point of an arbitrary point P2 and S1, S2, so P is between P1 and P2.

Thus, the half-line is closely associated with the concept Interval: An interval can be defined as the intersection of two half-lines.

Analytical representation

In analytic geometry, the half-line [AB the set of all points X whose position vector is given by corresponding

In this case, and the position vectors of the end points A and B. is the (real) parameter, this parameter equation.