braidings

Braidings, in general, are interlaced arrangements of two or more strands that form a single, cohesive structure. They occur in crafts, fashion, and engineering, and they also appear as formal concepts in mathematics and physics under the broader term braid.

In textiles and cordage, braiding produces flat or tubular patterns by passing strands over and under one another. Common forms include three-strand braids, four- and five-strand variants, and decorative patterns such as fishtail or kumihimo braids. Braided cords are valued for strength, flexibility, and resistance to unraveling, and are used for belts, laces, ropes, and trims.

In hair styling, braids tighten and protect hair while creating varied textures. Techniques range from simple plaits to complex cornrows, French braids, and Dutch braids; different styles carry cultural, aesthetic, and practical significance in many communities.

In mathematics, braid theory studies braids as geometric objects with an algebraic structure. The braid group B_n encodes braids on n strands through generators and relations, and closing braids yields links and knots. In physics, braiding operations of certain quasiparticles, such as anyons, are explored for potential applications in fault-tolerant quantum computation.

Braiding has ancient origins across cultures, evident in textile production and personal adornment. The term derives from Old English breodian, from Proto-Germanic roots, reflecting long-standing human engagement with interlaced patterns.