A reflection is a map that transforms an object into its mirror image with respect to a "mirror", which is a hyperplane of fixed points in the geometry. For example, a reflection of the small English letter p in respect to a vertical line would look like q. In order to reflect a planar figure one needs the "mirror" to be a line (axis of reflection or axis of symmetry), while for reflections in the three-dimensional space one would use a plane (the plane of reflection or symmetry) for a mirror. Reflection may be considered as the limiting case of inversion as the radius of the reference circle increases without bound.
Reflection is considered to be an opposite motion since it changes the orientation of the figures it reflects.
Read more about this topic: Transformation (function)
Famous quotes containing the word reflection:
“What chiefly distinguishes the daily press of the United States from the press of all other countries is not its lack of truthfulness or even its lack of dignity and honor, for these deficiencies are common to the newspapers everywhere, but its incurable fear of ideas, its constant effort to evade the discussion of fundamentals by translating all issues into a few elemental fears, its incessant reduction of all reflection to mere emotion. It is, in the true sense, never well-informed.”
—H.L. (Henry Lewis)
“Water. Its sunny track in the plain; its splashing in the garden canal, the sound it makes when in its course it meets the mane of the grass; the diluted reflection of the sky together with the fleeting sight of the reeds; the Negresses fill their dripping gourds and their red clay containers; the song of the washerwomen; the gorged fields the tall crops ripening.”
—Jacques Roumain (1907–1945)
“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)