what is the name of the curve made up of the points $(x,x^2...x^n)$ in $\mathbb {R}^n$ for all $x\in \mathbb R$??
For example: in $\mathbb R^2$ it would just be a parabola.
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I don't imagine it has a particular name? – copper.hat Nov 16 '13 at 05:22
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I think it does. – Asinomás Nov 16 '13 at 05:24
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http://www.nameacurve.com perhaps? – copper.hat Nov 16 '13 at 05:31
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Sorry, I was joking... (I was thinking star registry.) – copper.hat Nov 16 '13 at 05:33
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This is basically the rational normal curve of degree $n$. ("Basically" because the usual rational normal curve is $n$-dimensional projective space and has an additional point at infinity.)
Noam D. Elkies
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The curve of this form is known as the moment curve.
Asinomás
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Right $-$ indeed I see now that the Wikipedia page I linked to mentions that the affine locus of the rational normal curve is called the moment curve. – Noam D. Elkies Nov 16 '13 at 06:07
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