The moment curve in 
is the parametric curve
 |
for real 
. The convex hull of 
distinct points on this
curve is a cyclic polytope.
Its combinatorial type depends only on 
and 
,
not on the chosen parameter values (Medgyes 2026).
Moment Curve
See also
Convex Hull, Cyclic Polytope, Parametric CurveExplore with Wolfram|Alpha
References
Medgyes, C. "Inscribed 4-Polytopes of Maximal Volume with Seven and Eight Vertices." 12 Oct 2026. https://arxiv.org/abs/2610.26886.Ziegler, G. M. Lectures on Polytopes. New York: Springer-Verlag, 1995. https://doi.org/10.1007/978-1-4613-8431-1.Cite this as:
Weisstein, Eric W. "Moment Curve." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MomentCurve.html