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.
Read more about this topic: Screw Theory
Famous quotes containing the words screws and/or reflection:
“Each of us is full of too many wheels, screws and valves to permit us to judge one another on a first impression or by two or three external signs.”
—Anton Pavlovich Chekhov (1860–1904)
“Public morning diversions were the last dissipating habit she obtained; but when that was accomplished, her time was squandered away, the power of reflection was lost, [and] her ideas were all centered in dress, drums, routs, operas, masquerades, and every kind of public diversion. Visionary schemes of pleasure were continually present to her imagination, and her brain was whirled about by such a dizziness that she might properly be said to labor under the distemper called the vertigo.”
—Sarah Fielding (1710–1768)