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:
“Men should pledge themselves to nothing; for reflection makes a liar of their resolution.”
—Sophocles (497–406/5 B.C.)
“If the contemplation, even of inanimate beauty, is so delightful; if it ravishes the senses, even when the fair form is foreign to us: What must be the effects of moral beauty? And what influence must it have, when it embellishes our own mind, and is the result of our own reflection and industry?”
—David Hume (1711–1776)
“A little reflection will enable any person to detect in himself that setness in trifles which is the result of the unwatched instinct of self-will and to establish over himself a jealous guardianship.”
—Harriet Beecher Stowe (1811–1896)