Cyclic

Cyclic is an adjective derived from the Greek kyklos, meaning circle or ring. It is used to describe entities that occur in repeating sequences or have a ring-like structure.

In mathematics, cyclic describes objects that can be generated by a single element under a binary operation. A cyclic group is generated by one element; finite cyclic groups are isomorphic to the integers modulo n, while the infinite cyclic group is isomorphic to the integers under addition. A cyclic permutation is a permutation that forms a single cycle, and a cyclic graph is one in which the vertices lie on a single cycle.

In chemistry, cyclic compounds consist of atoms connected to form rings. The term distinguishes rings from open-chain (acyclic) structures. Cycloalkanes (such as cyclohexane) and arenes (such as benzene) are common examples; ring size and aromaticity affect properties and reactivity.

In biology and medicine, cyclic describes processes that repeat, such as the cell cycle and circadian rhythms. In pharmacology and biochemistry, cyclic peptides are peptides whose amino acids form a ring, which can confer stability and specific biological properties.

In computing and information theory, cyclic appears in cyclic data structures and in cycle-detection algorithms for graphs and lists that contain loops. Cyclic redundancy checks (CRCs) are error-detecting codes used in networks and storage devices to verify data integrity.

In arts and literature, cyclical forms employ recurring motifs or structures, creating a sense of return or repetition. Across disciplines, cyclic emphasizes repetition, enclosure, or ring-like organization.