defined using the convex hull of a cross-section of the hull of the vessel. It differs from the skin girth, the perimeter of the cross-section itself, except for boats and ships that have a convex hull. Ethology The convex hull is commonly known as the minimum convex polygon in ethology, the study of animal behavior, where it is a classic, though perhaps simplistic, approach in estimating an animal's home range based on points where the animal has been observed. Outliers can make the minimum convex polygon excessively large, which has motivated relaxed approaches that contain only a subset of the observations, for instance by choosing one of the convex layers that is close to a target percentage of the samples, or in the local convex hull method by combining convex hulls of neighborhoods of points. Quantum physics In quantum physics, the state space of any quantum system — the set of all ways the system can be prepared — is a convex hull whose extreme points are positive-semidefinite operators known as pure states and whose interior points are called mixed states. The Schrödinger–HJW theorem proves that any mixed state can in fact be written as a convex combination of pure states in multiple ways. Thermodynamics A convex hull in thermodynamics was identified by Josiah Willard Gibbs (1873), although the paper was published before the convex hull was so named. In a set of energies of several stoichiometries of a material, only those measurements on the lower convex hull will be stable. When removing a point from the hull and then calculating its distance to the hull, its distance to the new hull represents the degree of stability of the phase. History The lower convex hull of points in the plane appears, in the form of a Newton polygon, in a letter from Isaac Newton to Henry Oldenburg in 1676. The term "convex hull" itself appears as early as the work of , and the corresponding term in German appears earlier, for instance in Hans Rademacher's review of . Other terms, such as "convex envelope", were also used in this time frame. By 1938, according to Lloyd Dines, the term "convex hull" had become standard; Dines adds that he finds the term unfortunate, because the colloquial meaning of the word "hull" would suggest that it refers to the surface of a shape, whereas the convex hull includes the interior and not