Editing Screw theory (section)

== Screws by reflection ==
In [[transformation geometry]], the elemental concept of transformation is the [[reflection (mathematics)]]. In planar transformations a translation is obtained by reflection in parallel lines, and rotation is obtained by reflection in a pair of intersecting lines. To produce a screw transformation from similar concepts one must use planes in [[space]]: the parallel planes must be perpendicular to the [[screw axis]], which is the line of intersection of the intersecting planes that generate the rotation of the screw. Thus four reflections in planes effect a screw transformation. The tradition of [[inversive geometry]] borrows some of the ideas of [[projective geometry]] and provides a language of transformation that does not depend on [[analytic geometry]].