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.
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Famous quotes containing the words rational, normal and/or curve:
“No crime can ever be defended on rational grounds.”
—Titus Livius (Livy)
“The normal present connects the past and the future through limitation. Contiguity results, crystallization by means of solidification. There also exists, however, a spiritual present that identifies past and future through dissolution, and this mixture is the element, the atmosphere of the poet.”
—Novalis [Friedrich Von Hardenberg] (1772–1801)
“In philosophical inquiry, the human spirit, imitating the movement of the stars, must follow a curve which brings it back to its point of departure. To conclude is to close a circle.”
—Charles Baudelaire (1821–1867)