Mathematics and statistics

Centerpoint theorem

The centerpoint theorem is a result in discrete geometry: any n points in d dimensions have a point contained in every halfspace holding at least n/(d+1) of them.

Central carrier

The central carrier, also called central support or central cover, is the smallest projection in the center of a von Neumann algebra that dominates a given projection or operator.

Central composite design

The central composite design (CCD), also called the Box–Wilson design, is a response surface design of experiments, introduced by Box and Wilson in 1951 and widely used to fit quadratic models.

The central limit theorem (CLT) is a probability theorem stating that standardized sums of many independent random variables converge to a normal distribution regardless of their shape, underpinning parametric statistics.

Central moment

A central moment, or moment about the mean, of a random variable measures the distribution's shape about its own center; the variance, skewness, and kurtosis are scaled central moments.

Central symmetry

Central symmetry, also called point reflection, is a geometric transformation sending every point to its opposite through a fixed center; in the plane it is a 180° rotation.

Central tendency

Central tendency is the property of a data set by which one value stands for the whole distribution, measured most commonly by the mean, median, and mode.

Centroid

The centroid, also called the geometric center, is the mean position of a set of points; in a triangle it is where the three medians meet.

Cesàro summation

Cesàro summation, also called Cesàro mean, is a method of assigning sums to divergent series by taking limits of averaged partial sums, introduced by Ernesto Cesàro in 1890.

Cevian

A cevian is a line segment joining a triangle's vertex to a non-vertex point on the line of the opposite side, named for the Italian mathematician Giovanni Ceva.

CHAID

CHAID (Chi-squared Automatic Interaction Detection) is a decision tree technique, introduced by G. V. Kass in 1980, that splits categorical data into multiway groups using chi-square tests.

Chain mediation model

A chain mediation model, also called serial mediation, is a statistical model where an independent variable affects a dependent variable through two or more mediators in sequence.

Chain rule

The chain rule, also called differentiation by substitution, is the calculus rule giving the derivative of a composition of functions as the product of the rates.

Chain sampling

Chain sampling is an attribute acceptance sampling plan that accepts a lot using its sample result together with results from preceding lots, suited to destructive or expensive testing.

Chaitin's constant

Chaitin's constant, also called the halting probability or Chaitin's Omega, is a real number introduced by Gregory Chaitin in 1975 whose first n bits solve the halting problem for programs of length n.

Champernowne constant

The Champernowne constant, formed by writing the positive integers in order as 0.123456789101112..., is normal in base 10, proved by David Champernowne in 1933.

Chance-constrained programming

Chance-constrained programming, introduced by Charnes and Cooper in 1959, is a stochastic optimization method where constraints must hold with at least a specified probability, used in finance, power systems, and scheduling.

Chang and Roberts algorithm

The Chang and Roberts algorithm, also called the Chang–Roberts or LCR algorithm, elects a leader among processes arranged in a unidirectional ring, using O(n²) messages worst case.

Change of basis

Change of basis, also called a coordinate change, converts vector coordinates and matrices of linear maps between bases of a vector space using an invertible matrix.

Change of rings

Change of rings is a body of results in homological algebra comparing module invariants such as projective dimension, Tor, and Ext before and after a base ring is changed.

Change of support

Change of support, also called the change of support problem (COSP), is the geostatistical problem of predicting values at points or blocks whose support differs from the data's.

Change of variables for random variables

The change of variables for random variables is a formula giving the density of Y = g(X) from the density of X, using the Jacobian of the inverse transformation.

Change-point analysis

Change-point analysis is a statistical method for detecting where a time series or ordered dataset changes, estimating the number, locations, and sizes of changes, with roots in industrial quality control.

Change-point detection

Change-point detection comprises statistical methods for identifying when the distribution of a data series changes, using online procedures that alarm quickly or offline procedures that segment the series.

Channel capacity

Channel capacity, also known as information capacity, is the maximum rate for transmitting information over a communication channel with arbitrarily small error, introduced by Claude Shannon in 1948.

Chaos game

The chaos game is an algorithm that generates fractals by repeatedly moving a point partway toward a randomly chosen polygon vertex, credited to Michael Barnsley in 1988.

Chaos theory

Chaos theory, or deterministic chaos, is the branch of mathematics and physics that studies deterministic systems whose outcomes are so sensitive to initial conditions that long-range prediction becomes impractical.

Character theory

Character theory studies finite groups through characters, trace functions attached to representations. Created by Georg Frobenius in 1896, it remains a standard tool in group theory, physics, and chemistry.

Character variety

A character variety, also called the Betti moduli space, is a space parametrizing conjugacy classes of representations of a group into a Lie group, central to 3-manifold topology.