Editing Convex hull (section)

===Mathematics===
[[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}}
In [[discrete geometry]], both [[Radon's theorem]] and [[Tverberg's theorem]] concern the existence of partitions of point sets into subsets with intersecting convex hulls.{{sfnp|Reay|1979}}

The definitions of a convex set as containing line segments between its points, and of a convex hull as the intersection of all convex supersets, apply to [[hyperbolic space]]s as well as to Euclidean spaces. However, in hyperbolic space, it is also possible to consider the convex hulls of sets of [[ideal point]]s, points that do not belong to the hyperbolic space itself but lie on the boundary of a model of that space. The boundaries of convex hulls of ideal points of three-dimensional hyperbolic space are analogous to [[ruled surface]]s in Euclidean space, and their metric properties play an important role in the [[geometrization conjecture]] in [[low-dimensional topology]].{{sfnp|Epstein|Marden|1987}} Hyperbolic convex hulls have also been used as part of the calculation of [[Canonical form|canonical]] [[Triangulation (geometry)|triangulations]] of [[hyperbolic manifold]]s, and applied to determine the equivalence of [[Knot (mathematics)|knots]].{{sfnp|Weeks|1993}}

See also the section on [[#Brownian motion|Brownian motion]] for the application of convex hulls to this subject, and the section on [[#Space curves|space curves]] for their application to the theory of [[developable surface]]s.