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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