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:
“With respect to a true culture and manhood, we are essentially provincial still, not metropolitan,—mere Jonathans. We are provincial, because we do not find at home our standards; because we do not worship truth, but the reflection of truth; because we are warped and narrowed by an exclusive devotion to trade and commerce and manufacturers and agriculture and the like, which are but means, and not the end.”
—Henry David Thoreau (1817–1862)
“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)
“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)