Tufts of straight lines

A line bundle is a special set of lines in space or plane .

Tufts of straight lines in space

One speaks of a straight line bundle in space when all straight lines run through a common point, the bundle or carrier point , and lie in a common plane , which is referred to as the carrier plane of this straight line bundle. If the tuft or carrier point is at infinity, a parallel tuft of straight lines is created as a special case of the straight tuft .

The tuft of lines is one of the seven basic structures of synthetic projective geometry .

Line bundles in the 2-dimensional Cartesian coordinate system

Line tufts in the plane with a common point of intersection

One speaks of a straight line in the plane if all straight lines run through a common point in this plane, the line point . A pencil of lines can thus also as a special case of a family of functions linear functions to be construed. A line tuft with the tuft point is described by the following tuft equation: ${\displaystyle (a|b)}$

${\displaystyle y_{\text{(m,x)}}=m\cdot (x-a)+b}$

Another special case of a straight line is when the line point is at the origin of a Cartesian coordinate system . In this case the tuft equation is , where the parameter stands for the slope of the straight line . All straight lines of this cluster are thus also straight lines through the origin . ${\displaystyle y=mx}$ ${\displaystyle m}$

Individual evidence

1. ↑ Kleine Enzyklopädie Mathematik , Leipzig 1970, p. 216.