A zigzag is a

pattern A pattern is a regularity in the world, in human-made design, or in abstract ideas. As such, the elements of a pattern repeat in a predictable manner. A geometric pattern is a kind of pattern formed of geometric shapes and typically repeated l ...

made up of small corners at variable angles, though constant within the zigzag, tracing a path between two

parallel lines In geometry, parallel lines are coplanar infinite straight lines that do not intersect at any point. Parallel planes are planes in the same three-dimensional space that never meet. '' Parallel curves'' are curves that do not touch each oth ...

; it can be described as both jagged and fairly regular. In

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

, this pattern is described as a

skew apeirogon In geometry, an infinite skew polygon or skew apeirogon is an infinite 2-polytope with vertices that are not all Collinearity, colinear. Infinite zig-zag skew polygons are 2-dimensional infinite skew polygons with vertices alternating between two ...

. From the point of view of

symmetry Symmetry () in everyday life refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is Invariant (mathematics), invariant und ...

, a regular zigzag can be generated from a simple motif like a

line segment In geometry, a line segment is a part of a line (mathematics), straight line that is bounded by two distinct endpoints (its extreme points), and contains every Point (geometry), point on the line that is between its endpoints. It is a special c ...

by repeated application of a

glide reflection In geometry, a glide reflection or transflection is a geometric transformation that consists of a reflection across a hyperplane and a translation ("glide") in a direction parallel to that hyperplane, combined into a single transformation. Bec ...

. Although the origin of the word is unclear, its first printed appearances were in French-language books and

ephemera Ephemera are items which were not originally designed to be retained or preserved, but have been collected or retained. The word is etymologically derived from the Greek ephēmeros 'lasting only a day'. The word is both plural and singular. On ...

of the late 17th century.

Examples of zigzags

* The trace of a

triangle wave A triangular wave or triangle wave is a non-sinusoidal waveform named for its triangular shape. It is a periodic, piecewise linear, continuous real function. Like a square wave, the triangle wave contains only odd harmonics. However, t ...

or a

sawtooth wave The sawtooth wave (or saw wave) is a kind of non-sinusoidal waveform. It is so named based on its resemblance to the teeth of a plain-toothed saw with a zero rake angle. A single sawtooth, or an intermittently triggered sawtooth, is called a ...

is a zigzag. *

Pinking shears Pinking shears are scissors with saw-toothed blades instead of straight blades. They produce a zigzag pattern instead of a straight edge. Before pinking scissors were invented, a pinking punch or pinking iron was used to punch out a decorative ...

are designed to cut cloth or paper with a zigzag edge, to lessen fraying. * In sewing, a ''

zigzag stitch A zigzag stitch is variant geometry of the lockstitch. It is a back-and-forth stitch used where a straight stitch will not suffice, such as in reinforcing buttonholes, in stitching stretchable fabrics, and in temporarily joining two work pieces e ...

'' is a

machine A machine is a physical system that uses power to apply forces and control movement to perform an action. The term is commonly applied to artificial devices, such as those employing engines or motors, but also to natural biological macromol ...

stitch in a zigzag pattern. * The zigzag arch is an architectural embellishment used in

Islamic Islam is an Abrahamic religions, Abrahamic monotheistic religion based on the Quran, and the teachings of Muhammad. Adherents of Islam are called Muslims, who are estimated to number Islam by country, 2 billion worldwide and are the world ...

Byzantine The Byzantine Empire, also known as the Eastern Roman Empire, was the continuation of the Roman Empire centred on Constantinople during late antiquity and the Middle Ages. Having survived the events that caused the fall of the Western Roman E ...

Norman Norman or Normans may refer to: Ethnic and cultural identity * The Normans, a people partly descended from Norse Vikings who settled in the territory of Normandy in France in the 9th and 10th centuries ** People or things connected with the Norma ...

and

Romanesque architecture Romanesque architecture is an architectural style of medieval Europe that was predominant in the 11th and 12th centuries. The style eventually developed into the Gothic style with the shape of the arches providing a simple distinction: the Ro ...

. * In

seismology Seismology (; from Ancient Greek σεισμός (''seismós'') meaning "earthquake" and -λογία (''-logía'') meaning "study of") is the scientific study of earthquakes (or generally, quakes) and the generation and propagation of elastic ...

, earthquakes recorded in a "zigzag line" form by using

seismograph A seismometer is an instrument that responds to ground displacement and shaking such as caused by quakes, volcanic eruptions, and explosions. They are usually combined with a timing device and a recording device to form a seismograph. The out ...

References

Bibliography

* {{commons category Patterns Line (geometry)

Examples of zigzags

See also

References

Bibliography