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)
“And since the average lifetime—the relative longevity—is far greater for memories of poetic sensations than for those of heartbreaks, since the very long time that the grief I felt then because of Gilbert, it has been outlived by the pleasure I feel, whenever I wish to read, as in a sort of sundial, the minutes between twelve fifteen and one o’clock, in the month of May, upon remembering myself chatting ... with Madame Swann under the reflection of a cradle of wisteria.”
—Marcel Proust (1871–1922)