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:
“It is conceivable at least that a late generation, such as we presumably are, has particular need of the sketch, in order not to be strangled to death by inherited conceptions which preclude new births.... The sketch has direction, but no ending; the sketch as reflection of a view of life that is no longer conclusive, or is not yet conclusive.”
—Max Frisch (1911–1991)
“Much of what passes for quality on British television is no more than a reflection of the narrow elite which controls it and has always thought that its tastes were synonymous with quality.”
—Rupert Murdoch (b. 1931)
“With some people solitariness is an escape not from others but from themselves. For they see in the eyes of others only a reflection of themselves.”
—Eric Hoffer (1902–1983)