Editing Simplex (section)

== Applications ==
* In [[statistics]], simplices are sample spaces of [[compositional data]] and are also used in plotting quantities that sum to 1, such as proportions of subpopulations, as in a [[ternary plot]].
* In [[probability theory]], a simplex space is often used to represent the space of probability distributions. The [[Dirichlet distribution]], for instance, is defined on a simplex.
* In [[applied statistics#industrial|industrial statistics]], simplices arise in problem formulation and in algorithmic solution. In the design of bread, the producer must combine yeast, flour, water, sugar, etc. In such [[mixture]]s, only the relative proportions of ingredients matters: For an optimal bread mixture, if the flour is doubled then the yeast should be doubled. Such mixture problem are often formulated with normalized constraints, so that the nonnegative components sum to one, in which case the feasible region forms a simplex. The quality of the bread mixtures can be estimated using [[response surface methodology]], and then a local maximum can be computed using a [[nonlinear programming]] method, such as [[sequential quadratic programming]].<ref>
{{cite book
|author=Cornell, John
|title=Experiments with Mixtures: Designs, Models, and the Analysis of Mixture Data
|edition=third
|publisher=Wiley
|year=2002
|isbn=0-471-07916-2
}}</ref>
* In [[operations research]], [[linear programming]] problems can be solved by the [[simplex algorithm]] of [[George Dantzig]].
* In [[game theory]], strategies can be represented as points within a simplex. This representation simplifies the analysis of mixed strategies.
* In [[geometric design]] and [[computer graphics]], many methods first perform simplicial [[triangulation (topology)|triangulation]]s of the domain and then [[interpolation|fit interpolating]] [[polynomial and rational function modeling|polynomials]] to each simplex.<ref>{{cite journal | last = Vondran | first = Gary L. | date = April 1998 | title = Radial and Pruned Tetrahedral Interpolation Techniques | journal = HP Technical Report | volume = HPL-98-95 | pages = 1–32 | url = http://www.hpl.hp.com/techreports/98/HPL-98-95.pdf | access-date = 2009-11-11 | archive-date = 2011-06-07 | archive-url = https://web.archive.org/web/20110607102757/http://www.hpl.hp.com/techreports/98/HPL-98-95.pdf | url-status = dead }}</ref>
* In [[chemistry]], the hydrides of most elements in the [[p-block]] can resemble a simplex if one is to connect each atom. [[Neon]] does not react with hydrogen and as such is [[Monatomic gas|a point]], [[fluorine]] bonds with one hydrogen atom and forms a line segment, [[oxygen]] bonds with two hydrogen atoms in a [[Bent molecular geometry|bent]] fashion resembling a triangle, [[nitrogen]] reacts to form a [[Trigonal pyramidal molecular geometry|tetrahedron]], and [[carbon]] forms [[Tetrahedral molecular geometry|a structure]] resembling a [[Schlegel diagram]] of the 5-cell. This trend continues for the heavier analogues of each element, as well as if the hydrogen atom is replaced by a [[halogen]] atom.
* In some approaches to [[quantum gravity]], such as [[Regge calculus]] and [[causal dynamical triangulation]]s, simplices are used as building blocks of discretizations of spacetime; that is, to build [[simplicial manifold]]s.