# Cycle

## Cycle

Sequence of elements or pattern of a phenomena that repeats continuously.

The word cycle has different meanings depending on the domain where it is used. In math, we find this term among others in graph theory and in the study of periodic phenomena like trigonometric functions.

### Examples

• The cycle of the seasons.
• The respiratory cycle.
• The cycle of the phases of the Moon.

In an undirected graph a cycle is a chain that starts and ends at the same vertex.

In an undirected graph, the length of a cycle is the number of edges that make up this cycle.

### Example The chain that emerges from A and concludes at A, passing through B, C, D and E, is a cycle of length 5.

In the graphic representation of a trigonometric function, a cycle is a part of the graph that forms the pattern that repeats indefinitely.

The length of a cycle is the period of the corresponding trigonometric function.

### Example

In this illustration, the cycle of the function is the portion of its graph between the two vertices identified by the hollow points. 