There are many terms in mathematics that begin with cyclic: * Cyclic chain rule, for derivatives, used in thermodynamics *

Cyclic code In coding theory, a cyclic code is a block code, where the circular shifts of each codeword gives another word that belongs to the code. They are error-correcting codes that have algebraic properties that are convenient for efficient error detec ...

, linear codes closed under cyclic permutations * Cyclic convolution, a method of combining periodic functions *

Cycle decomposition (graph theory) In graph theory, a cycle decomposition is a decomposition (a partitioning of a graph's edges) into cycles. Every vertex in a graph that has a cycle decomposition must have even degree. Cycle decomposition of K_n and K_n-I Brian Alspach and Hea ...

* Cycle decomposition (group theory) *

Cyclic extension In abstract algebra, an abelian extension is a Galois extension whose Galois group is abelian. When the Galois group is also cyclic, the extension is also called a cyclic extension. Going in the other direction, a Galois extension is called solvabl ...

, a field extension with cyclic Galois group * Graph theory: *

Cyclic function A periodic function is a function that repeats its values at regular intervals. For example, the trigonometric functions, which repeat at intervals of 2\pi radians, are periodic functions. Periodic functions are used throughout science to d ...

, a periodic function **

Cycle graph In graph theory, a cycle graph or circular graph is a graph that consists of a single cycle, or in other words, some number of vertices (at least 3, if the graph is simple) connected in a closed chain. The cycle graph with vertices is called ...

, a connected, 2-regular graph **

Cycle graph (algebra) In group theory, a subfield of abstract algebra, a group cycle graph illustrates the various cycles of a group and is particularly useful in visualizing the structure of small finite groups. A cycle is the set of powers of a given group eleme ...

, a diagram representing the cycles determined by taking powers of group elements **

Circulant graph In graph theory, a circulant graph is an undirected graph acted on by a cyclic group of symmetries which takes any vertex to any other vertex. It is sometimes called a cyclic graph, but this term has other meanings. Equivalent definitions Cir ...

, a graph with cyclic symmetry **

Cycle (graph theory) In graph theory, a cycle in a graph is a non-empty trail in which only the first and last vertices are equal. A directed cycle in a directed graph is a non-empty directed trail in which only the first and last vertices are equal. A graph wit ...

, a nontrivial path in some graph from a node to itself ** Cyclic graph, a graph containing at least one graph cycle *

Cyclic group In group theory, a branch of abstract algebra in pure mathematics, a cyclic group or monogenous group is a group, denoted C''n'', that is generated by a single element. That is, it is a set of invertible elements with a single associative bi ...

, a group generated by a single element *

Cyclic homology In noncommutative geometry and related branches of mathematics, cyclic homology and cyclic cohomology are certain (co)homology theories for associative algebras which generalize the de Rham (co)homology of manifolds. These notions were independen ...

, an approximation of K-theory used in non-commutative differential geometry *

Cyclic module In mathematics, more specifically in ring theory, a cyclic module or monogenous module is a module over a ring that is generated by one element. The concept is a generalization of the notion of a cyclic group, that is, an Abelian group (i.e. Z ...

, a module generated by a single element *

Cyclic notation In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or pr ...

, a way of writing permutations *

Cyclic number A cyclic number is an integer for which cyclic permutations of the digits are successive integer multiples of the number. The most widely known is the six-digit number 142857, whose first six integer multiples are :142857 × 1 = 142857 :14 ...

, a number such that cyclic permutations of the digits are successive multiples of the number *

Cyclic order In mathematics, a cyclic order is a way to arrange a set of objects in a circle. Unlike most structures in order theory, a cyclic order is not modeled as a binary relation, such as "". One does not say that east is "more clockwise" than west. In ...

, a ternary relation defining a way to arrange a set of objects in a circle *

Cyclic permutation In mathematics, and in particular in group theory, a cyclic permutation (or cycle) is a permutation of the elements of some set ''X'' which maps the elements of some subset ''S'' of ''X'' to each other in a cyclic fashion, while fixing (that is, ...

, a permutation with one nontrivial orbit *

Cyclic polygon In geometry, the circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius. Not every polyg ...

, a polygon which can be given a circumscribed circle *

Cyclic shift In combinatorial mathematics, a circular shift is the operation of rearranging the entries in a tuple, either by moving the final entry to the first position, while shifting all other entries to the next position, or by performing the inverse ope ...

, also known as circular shift *

Cyclic symmetry In group theory, a branch of abstract algebra in pure mathematics, a cyclic group or monogenous group is a group, denoted C''n'', that is generated by a single element. That is, it is a set of invertible elements with a single associative binar ...

, n-fold rotational symmetry of 3-dimensional space

See also