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:
“There are three principal means of acquiring knowledge available to us: observation of nature, reflection, and experimentation. Observation collects facts; reflection combines them; experimentation verifies the result of that combination. Our observation of nature must be diligent, our reflection profound, and our experiments exact. We rarely see these three means combined; and for this reason, creative geniuses are not common.”
—Denis Diderot (1713–1784)
“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)
“Uncertainty about the outcome is a given in child rearing and not a reflection of a mother’s inadequacy. She should not be misled by her wish to be omnipotent, all-powerful, all-giving, the perfect mother, who will right all the wrongs and make up for all the deprivations of her own childhood. She is simply an imperfect human being with needs of her own.”
—Elaine Heffner (20th century)