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===Mathematics===
[[File:Tverberg heptagon.svg|thumb|upright|Partition of seven points into three subsets with intersecting convex hulls, guaranteed to exist for any seven points in the plane by [[Tverberg's theorem]]]]▼
[[Newton polygon]]s of univariate [[polynomial]]s and [[Newton polytope]]s of multivariate polynomials are convex hulls of points derived from the exponents of the terms in the polynomial, and can be used to analyze the [[asymptotic analysis|asymptotic]] behavior of the polynomial and the valuations of its roots.<ref>{{harvtxt|Artin|1967}}; {{harvtxt|Gel'fand|Kapranov|Zelevinsky|1994}}</ref> Convex hulls and polynomials also come together in the [[Gauss–Lucas theorem]], according to which the [[Zero of a function|roots]] of the derivative of a polynomial all lie within the convex hull of the roots of the polynomial.{{sfnp|Prasolov|2004}}
▲[[File:Tverberg heptagon.svg|thumb|upright|Partition of seven points into three subsets with intersecting convex hulls, guaranteed to exist for any seven points in the plane by [[Tverberg's theorem]]]]
In [[Spectral theory|spectral analysis]], the [[numerical range]] of a [[normal matrix]] is the convex hull of its [[eigenvalue]]s.{{sfnp|Johnson|1976}}
The [[Russo–Dye theorem]] describes the convex hulls of [[unitary element]]s in a [[C*-algebra]].{{sfnp|Gardner|1984}}
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