In mathematics, the rational normal curve is a smooth, rational curve of degree n in projective n-space It is a simple example of a projective variety; formally, it is the Veronese variety when the domain is the projective line. For n=2 it is the flat conic and for n=3 it is the twisted cubic. The term "normal" is an old term meaning that the linear system defining the embedding is complete (and has nothing to do with normal schemes). The intersection of the rational normal curve with an affine space is called the moment curve.
Read more about Rational Normal Curve: Definition, Alternate Parameterization, Properties
Famous quotes containing the words rational, normal and/or curve:
“No actual skeptic, so far as I know, has claimed to disbelieve in an objective world. Skepticism is not a denial of belief, but rather a denial of rational grounds for belief.”
—William Pepperell Montague (1842–1910)
“Everyone in the full enjoyment of all the blessings of his life, in his normal condition, feels some individual responsibility for the poverty of others. When the sympathies are not blunted by any false philosophy, one feels reproached by one’s own abundance.”
—Elizabeth Cady Stanton (1815–1902)
“I have been photographing our toilet, that glossy enameled receptacle of extraordinary beauty.... Here was every sensuous curve of the “human figure divine” but minus the imperfections. Never did the Greeks reach a more significant consummation to their culture, and it somehow reminded me, in the glory of its chaste convulsions and in its swelling, sweeping, forward movement of finely progressing contours, of the Victory of Samothrace.”
—Edward Weston (1886–1958)