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 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 other or interse ...

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

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...

, 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 colinear. Infinite zig-zag skew polygons are 2-dimensional infinite skew polygons with vertices alternating between two parallel l ...

. From the point of view of

symmetry Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definit ...

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

line segment In geometry, a line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints. The length of a line segment is given by the Euclidean distance between i ...

by repeated application of a

glide reflection In 2-dimensional geometry, a glide reflection (or transflection) is a symmetry operation that consists of a reflection over a line and then translation along that line, combined into a single operation. The intermediate step between reflectio ...

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

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 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 hem on ...

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

sewing Sewing is the craft of fastening or attaching objects using stitches made with a sewing needle and thread. Sewing is one of the oldest of the textile arts, arising in the Paleolithic era. Before the invention of spinning yarn or weaving fabri ...

, 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 ed ...

'' is a

machine A machine is a physical system using 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 macromolecules ...

stitch in a zigzag pattern. The zigzag arch is an

architectural Architecture is the art and technique of designing and building, as distinguished from the skills associated with construction. It is both the process and the product of sketching, conceiving, planning, designing, and constructing buildings o ...

embellishment used in

Islamic Islam (; ar, ۘالِإسلَام, , ) is an Abrahamic monotheistic religion centred primarily around the Quran, a religious text considered by Muslims to be the direct word of God (or ''Allah'') as it was revealed to Muhammad, the main ...

Byzantine The Byzantine Empire, also referred to as the Eastern Roman Empire or Byzantium, was the continuation of the Roman Empire primarily in its eastern provinces during Late Antiquity and the Middle Ages, when its capital city was Constantinopl ...

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 10th and 11th centuries ** People or things connected with the Norm ...

and

Romanesque architecture Romanesque architecture is an architectural style of medieval Europe characterized by semi-circular arches. There is no consensus for the beginning date of the Romanesque style, with proposals ranging from the 6th to the 11th century, this later ...

References

Bibliography

* {{commons category Patterns

Examples of zigzags

See also

References

Bibliography