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Braid

A braid is a length of cord, ribbon, or hair formed by interlacing three or more strands of flexible material in a regular diagonal pattern.^[1] This structure is created by repeatedly crossing the strands over and under one another in a specific sequence, resulting in a woven appearance that can be flat, round, or three-dimensional depending on the technique.^[2] Braids serve both practical and decorative purposes across various fields, including hairstyling, textiles, crafts, and culinary arts.^[3] In hairstyling, they are a versatile technique used to organize and adorn hair, with origins tracing back potentially to the Paleolithic era, as suggested by interpretations of the Venus of Willendorf figurine from around 25,000 BCE, where the head may depict braided or plaited hair.^[4] Culturally, braids have signified social status, identity, and rites in diverse societies, from ancient African communities where they encoded messages or denoted rank, to European and Asian traditions incorporating them into daily and ceremonial wear.^[5] Beyond personal adornment, braids appear in rope-making for strength and durability, as well as in decorative trims like gold braid on military uniforms to indicate rank or branch of service.^[6] In mathematics and topology, a braid is conceptualized as a geometric configuration of strands fixed at two parallel boundaries that interweave without reversing direction, forming the basis for braid theory.^[7] Braid groups, which capture the algebraic relations among these configurations, have significant applications in knot theory, quantum physics, and computer science, including models for particle interactions and DNA recombination.^[8]^[9] This abstract framework, developed in the early 20th century by mathematicians like Emil Artin, underscores the braid's role as a fundamental object in modern scientific inquiry.^[10]

Human and Cultural Uses

Hair Braiding

Hair braiding, the practice of intertwining strands of human hair to create structured patterns, dates back to ancient civilizations. In Egypt around 3000 BCE, skilled hairdressers crafted wigs by braiding human hair into numerous small plaits, as evidenced by artifacts and tomb reliefs depicting these styles on both men and women.^[11] Similarly, archaeological findings from Hierakonpolis reveal hair extensions used for braiding as early as 3400 BCE, indicating early techniques for enhancing and styling natural hair.^[12] In Africa, braiding traditions extend to at least 3500 BCE, with intricate styles such as those resembling modern box braids appearing in ancient societies for practical and symbolic purposes, as suggested by rock art and artifacts.^[13] These early practices, seen in mummies and rock art across the continent, highlight braiding's role in daily life and adornment long before written records. Various techniques define hair braiding, each involving systematic weaving to achieve distinct looks. The three-strand braid, a foundational method, begins by dividing a section of hair into three equal parts; the stylist then crosses the right strand over the middle one, followed by the left strand over the new middle, repeating until the end while maintaining even tension.^[14] Cornrows, a close-to-the-scalp style common in African traditions, start with parting the hair into rows using a comb; hair is gathered in small sections and woven underhand by passing strands alternately beneath the central piece, creating flat, raised tracks that lie against the head.^[15] French braiding builds on the three-strand approach by starting at the crown and progressively incorporating additional hair from the sides into the outer strands with each cross-over, resulting in a voluminous, integrated plait that gathers more hair as it descends.^[16] Box braids involve sectioning the hair into square or rectangular parts, adding synthetic extensions to the natural hair, and twisting or weaving three strands tightly from the roots to form uniform, cylindrical ropes that extend several inches beyond the ends.^[17] In many African tribes, braids function as status symbols, conveying information about social position, age, and role within the community. For instance, among groups like the Yoruba and Igbo, specific patterns in cornrows or warrior braids denoted rank, with elaborate designs reserved for leaders or fighters to signify strength and heritage.^[18] These hairstyles, often taking hours to complete, reflected tribal identity and were used in rituals or battles to inspire morale.^[19] In Indigenous communities, such as those of the Diné (Navajo) and other Native American groups, braiding serves as a means of social bonding, where communal grooming sessions strengthen familial and cultural ties through shared storytelling and care.^[20]^[21] This practice fosters emotional connections, preserving traditions passed down through generations.^[21] Modern hair braiding relies on specialized tools and materials to facilitate precise and durable styles. Rat-tail combs, with their long, thin handles, are essential for clean partings and sectioning, allowing stylists to create even rows or patterns on the scalp.^[22] Beads made of plastic, wood, or metal add decorative elements, threaded onto the ends of braids to enhance aesthetics and cultural expression, while hair extensions—typically synthetic fibers or human hair—extend length and volume for styles like box braids.^[23] These materials, combined with holding sprays or oils, ensure longevity without compromising hair integrity.^[22] When performed tension-free, hair braiding offers health benefits, including scalp protection from environmental damage and promotion of hair growth. Protective styles like cornrows or box braids shield strands from friction, UV exposure, and manipulation, helping retain moisture and reduce breakage to support length retention over time.^[24] Gentle braiding minimizes traction on follicles, preventing conditions like alopecia while allowing the scalp to breathe and encouraging nutrient delivery for healthier growth.^[25]^[26] However, excessive tightness can lead to scalp irritation, underscoring the importance of professional application.^[27]

Decorative and Textile Braids

Decorative and textile braids encompass a diverse array of interlaced structures created from flexible materials, primarily for aesthetic enhancement in clothing, accessories, and crafts. These braids differ from functional ropes by emphasizing intricate patterns and ornamental qualities, often involving multi-strand techniques that produce symmetrical or repeating motifs. Historically rooted in various cultures, they serve both artistic and utilitarian roles, such as trimming garments or forming jewelry components. One prominent type is kumihimo, a traditional Japanese braiding method originating in the Heian period (794–1185 CE), where multiple strands—typically silk cords—are interlaced on a loom-like device called a marudai or takadai to form flat or round braids.^[28] This technique, known as karakumi in its early flat form, combines elements of braiding and weaving using paired strands to achieve symmetrical patterns, often finished with tassels for decorative appeal.^[28] Similarly, Celtic knot braids draw from ancient interlacing designs that emerged in the 3rd–4th centuries CE, influenced by Roman interlace patterns and later adapted into Insular art for textiles and metalwork.^[29] These knots feature continuous, looping strands without clear beginnings or ends, symbolizing eternity, and were incorporated into embroidered fabrics and woven accessories during the medieval era.^[29] In medieval Europe, braided laces, or "points," were essential for securing clothing elements like hose to doublets, crafted from twisted or interlaced cords of linen or wool to provide both durability and subtle decoration.^[30] These evolved into more ornate uses in jewelry and garment trims by the 14th century, where braiders employed finger-loop methods to create narrow, patterned cords for lacing bodices or adorning belts.^[31] This tradition persisted into modern crafts, notably in friendship bracelets, which trace their origins to indigenous Central American knotting practices and gained popularity in the United States during the 1970s as symbols of camaraderie.^[32] Common materials for decorative braids include yarn for soft, colorful textiles; leather for sturdy accessories like belts or watchbands; and fine wire for metallic jewelry, each allowing distinct textures and durabilities.^[32] Techniques vary by material but often involve over-under interlacing: for instance, chevron patterns emerge from mirroring forward and backward knots in even-strand setups, creating V-shaped zigzags ideal for bracelets, while spiral designs result from uneven tension in four-strand braids, producing a helical twist suited to leather thongs.^[32] Contemporary applications blend these traditions with macramé-inspired braids, where knotted cords of cotton or synthetic yarns form bohemian fashion items like handbags, necklaces, and hair accessories, reviving 1970s aesthetics in sustainable, handmade designs.^[33] These modern pieces emphasize eco-friendly materials and customizable patterns, appearing in high-street jewelry and artisanal markets as versatile accents for everyday wear.^[33]

Industrial and Practical Applications

Ropes and Cables

Braided ropes and cables have been essential for load-bearing applications since ancient times, with evidence of hemp-based constructions dating back to around 8000 BCE in Mesopotamia, where fibers were twisted and woven into durable strands for hauling and binding.^[34] These early ropes, often made from natural materials like hemp, flax, and sisal, provided the tensile strength needed for tasks such as construction and agriculture, evolving through trial and error to incorporate braiding techniques that enhanced durability under tension.^[35] Modern rope construction methods build on these foundations, employing techniques like laid, plaited, and kernmantle designs to optimize tensile strength. Laid ropes consist of three or more strands twisted together in opposing directions, creating a balanced structure that resists unraveling while distributing load across the fibers.^[36] Plaited ropes, a form of braiding, interweave multiple strands—often eight or more—in a crisscross pattern, which allows for greater flexibility and even stress distribution compared to simple twisting.^[37] Kernmantle ropes feature a braided outer sheath (mantle) encasing a core of parallel or twisted yarns (kern), where the core bears most of the load for high tensile strength, and the sheath protects against abrasion.^[38] The shift from natural to synthetic materials accelerated post-World War II, with nylon emerging as a groundbreaking fiber in the late 1930s and gaining widespread use in ropes by the 1940s due to its superior strength-to-weight ratio and elasticity. Subsequent developments included polyester in the 1950s for low-stretch mooring lines, polypropylene in the 1950s for lightweight and buoyant options, and high-performance fibers like aramids (e.g., Kevlar) and ultra-high-molecular-weight polyethylene (UHMWPE, e.g., Dyneema) from the 1960s-1980s for exceptional strength and cut resistance.^[39] This evolution enabled ropes to handle heavier loads with less bulk, as seen in applications like maritime ship rigging, where braided nylon cables secure sails and moor vessels against dynamic forces; climbing, where kernmantle designs absorb falls; and construction, for lifting materials in cranes and scaffolding.^[40] For instance, a 1-inch diameter double-braided nylon rope typically achieves a breaking strength of around 10,000 kg, far surpassing traditional hemp equivalents.^[41] Braided constructions offer key advantages over purely twisted ropes, including reduced kinking during handling and more uniform stress distribution, which prevents localized failures and enhances overall longevity under repeated loading.^[42] This makes them ideal for industrial uses requiring reliability, though related braiding techniques also appear in electrical shielding for electromagnetic protection.^[43]

Electrical and Shielding Applications

Braided shielding plays a crucial role in electrical applications by providing electromagnetic interference (EMI) protection through interwoven metallic wires, typically copper or tinned copper, that form a flexible mesh around cable conductors. This construction, often referred to as a copper wire braid, creates a Faraday cage-like barrier that attenuates external electromagnetic fields and prevents signal leakage, essential for maintaining signal integrity in sensitive electronics. Coverage ratios, defined as the optical percentage of the braid that blocks light (indicating shielding density), typically range from 70% to 95%, with higher ratios like 85% offering superior EMI suppression for high-frequency applications.^[44]^[45] The development of braided shielding traces back to the late 19th century, when it was initially employed to insulate early telegraph and electrical wires against interference as these systems entered homes and businesses. By the early 20th century, advancements in telephony led to the 1929 patent by Lloyd Espenschied and Herman Affel for coaxial cables, which incorporated braided metallic shields to enable reliable long-distance transmission over open wires, marking a shift from simple spacing techniques to structured EMI mitigation. This evolved into modern coaxial cables used in telecommunications, where braided shields balance flexibility and protection, evolving alongside foil alternatives for comprehensive shielding in broadband and RF systems.^[46]^[47] In automotive wiring harnesses, braided shields encase bundles of wires to safeguard against EMI from ignition systems and motors, while their inherent flexibility accommodates the repeated bending and vibration in vehicle environments, enhancing durability over millions of cycles. Similarly, in audio equipment, such as microphone and instrument cables, braided copper meshes reduce noise and hum from external RF sources, preserving audio fidelity during dynamic use like stage performances, where the braid's suppleness prevents signal degradation from movement. These applications leverage the braid's mechanical strength, which adds tensile reinforcement without sacrificing bend radius, making it ideal for harnesses in confined spaces.^[48]^[49]^[50] Manufacturing braided sheaths for electrical cables primarily utilizes maypole or spiral braiding machines, which interlace carriers of wire around a central core at controlled speeds to form uniform patterns. In maypole machines, carriers follow a figure-eight path on a rotating bed, producing a diamond or regular weave with adjustable braid angles typically between 30° and 60° to optimize coverage and flexibility; steeper angles increase density but require more material. Spiral braiding, conversely, employs rotating spindles for helical application, allowing precise overlap control—often 15-20° for minimal gaps—suited for high-speed production of EMI shields in coaxial assemblies. These processes ensure low-resistance paths for grounding while maintaining the sheath's expandability for easy installation.^[51]^[52]^[53]

Culinary Uses

Onion and Garlic Braids

Onion and garlic braids are created by weaving the dried stems of harvested bulbs into strands, typically using a three-strand pattern on heavy-duty string or rope for easy hanging and display. After curing the bulbs in a dry, well-ventilated area for about a week to reduce moisture content, the tops are left intact while the bulbs are interlaced progressively, starting with one bulb per strand and crossing them like a French braid to secure the structure. This method works well for softneck garlic varieties and onions with flexible tops, allowing for braids of 10 to 20 bulbs or more, depending on the desired length.^[54]^[55] The practice originated as a traditional storage technique in Mediterranean and European farming communities, where it facilitated drying and preservation post-harvest to combat rot in humid climates. In regions like Italy and Sicily, farmers have long braided garlic and onions to utilize airflow around the spaced bulbs, a method documented in agricultural customs dating back centuries for maintaining crop quality through winter. Similar interlacing techniques for alliums appear in broader European rural traditions to ensure even drying and accessibility.^[56]^[57]^[58] Braiding provides key benefits for preservation, including enhanced airflow that circulates around each bulb to prevent moisture buildup and fungal growth, thereby deterring rot and common pests like mold or insects. The elevated hanging position further reduces ground contact and humidity exposure, allowing properly cured braids to store in cool, dark spaces for 6 to 12 months without significant sprouting or spoilage. Garlic's natural antimicrobial properties in the bulbs add an extra layer of pest resistance during extended storage.^[54]^[59]^[60] Culturally, onion and garlic braids serve as symbols of abundance and prosperity, often displayed during harvest festivals to celebrate successful yields and communal labor. In Italian traditions, such as those in Abruzzo, intricately braided garlic strands are showcased at local markets and events like the Red Garlic Festival in Sulmona, representing agricultural heritage and warding off misfortune. Similar displays appear in European harvest celebrations, where braids embody the fruits of the harvest and are hung in homes for protection and good fortune.^[57]^[61]

Braided Baked Goods

Braided baked goods feature intricate weaving of dough strands that enhance both their visual appeal and structural integrity during baking. For challah, this technique originated in 15th-century Central and Eastern Europe, where it became common for enriched Sabbath breads among Ashkenazi Jewish communities, evolving from earlier loaves into a distinctly ceremonial form.^[62]^[63] The plaited design symbolizes unity, with intertwined strands representing the cohesion of the Jewish people and the binding of physical life to the divine.^[64]^[65] Preparation begins with an enriched yeast dough, typically incorporating eggs, butter or oil, and sugar for tenderness. For challah, the risen dough is divided into three to six equal portions, each rolled into uniform strands about 12-14 inches long and slightly tapered at the ends to facilitate weaving. The strands are pinched firmly together at one end to secure the braid, then crossed over one another in a repeating pattern—such as pulling the outer strand under the middle for a three-strand version—until the opposite end, where the loose ends are pinched and tucked underneath for a neat finish.^[66]^[67] Brioche, a French enriched bread originating in Normandy in the 1400s, follows a similar braiding process, with its higher butter content making the dough softer; after dividing into strands, bakers braid tightly and pinch the ends to maintain shape, often forming a loaf or ring to accommodate the dough's richness.^[68]^[69]^[70] The braided loaf then undergoes a final proofing for 45-60 minutes until puffy, followed by an egg wash for shine and optional light scoring along the strands to guide expansion and add decorative flair.^[71] Beyond aesthetics, braiding provides practical advantages in baking. The interwoven structure offers stability to soft, enriched doughs prone to spreading, promoting even heat distribution for uniform cooking and a tender crumb without dense spots.^[72]^[73] This results in consistent baking times, typically 30-40 minutes at 350°F (175°C), yielding a golden crust while retaining internal moisture.^[74] Cultural variations highlight regional adaptations of this technique. Italian pane intrecciato, or braided bread, uses a simple three-strand plait from a lightly sweetened dough, proofed for about 1 hour after shaping, and baked at 350°F for 40 minutes to achieve a fluffy texture ideal for holidays.^[74] These examples underscore braiding's role in elevating everyday dough into festive, structurally sound pastries across traditions. In other regions, such as Latin America, braided breads like pan de yema incorporate similar weaving for holiday meals, adding to the global diversity of the practice.^[75]

Mathematical and Scientific Concepts

Braid Theory

In mathematics, braid theory is the topological study of braids, which are geometric objects consisting of a finite number of strands or curves embedded in three-dimensional space, connecting a fixed set of points on a top plane to corresponding points on a parallel bottom plane, considered up to ambient isotopy that preserves the endpoints.^[76] These strands do not intersect except possibly at the endpoints, and the isotopy ensures that the braids can be continuously deformed into one another without passing through each other or moving the fixed points.^[77] This framework extends classical knot theory by focusing on open-ended tangles rather than closed loops, allowing for the analysis of intertwining paths in a controlled geometric setting.^[78] The foundations of braid theory were established by Emil Artin in 1925 through his seminal work "Theorie der Zopfe," where he introduced braids as a means to classify and study these structures systematically, building directly on the emerging field of knot theory to address limitations in representing open tangles.^[79] Artin's approach formalized braids as equivalence classes under isotopy, providing tools to convert them into algebraic representations while preserving their topological essence.^[80] This development marked a pivotal shift, enabling deeper insights into the topology of three-dimensional embeddings that knot theory alone could not fully capture.^[81] Key properties of braids distinguish between Artin braids, which permit permutations of the strand endpoints (allowing strands to swap positions), and pure braids, a subgroup where each strand returns to its original endpoint without permutation, preserving the identity of individual paths.^[78] A fundamental operation in braid theory is the closure of a braid, achieved by connecting the top endpoints to the bottom ones via non-intersecting arcs outside the braid's space, resulting in a link or knot; Alexander's theorem (1923) guarantees that every oriented knot or link can be represented as the closure of some braid.^[82] For instance, a braid word— a sequence describing crossings—can be projected and closed to yield a standard knot diagram, facilitating the study of link invariants.^[83] These properties underpin the geometric foundations, with algebraic encodings via braid groups providing a complementary representation.^[84] Braid theory finds significant applications in physics, particularly in modeling the supercoiling of DNA molecules, where intertwined double helices behave as braids during replication and recombination, with closure operations simulating catenane formation.^[85] In quantum mechanics, braids describe the paths of anyonic particles in two-dimensional systems, where the topological braiding of worldlines encodes non-Abelian statistics robust against local perturbations, as explored in models of topological quantum computing.^[86] These applications highlight braid theory's role in bridging abstract topology with physical phenomena involving persistent entanglement.^[87]

Braid Groups

The braid group B_n on n strands is defined as the fundamental group of the unordered configuration space of n points in the Euclidean plane, capturing the homotopy classes of motions of these points without collisions.^[88] This topological interpretation, established through fibrations of configuration spaces, provides a geometric foundation for the group structure.^[89] Algebraically, B_n is presented by generators \sigma_i for i = 1, \dots, n-1, where each \sigma_i represents the positive crossing of the i-th strand over the (i+1)-th strand, with all other strands fixed.^[76] The defining relations, known as the Artin relations, govern the interactions between these generators. The braid relation for adjacent generators is

\sigma_i \sigma_{i+1} \sigma_i = \sigma_{i+1} \sigma_i \sigma_{i+1}

for i = 1, \dots, n-2, reflecting the equivalence of certain crossing sequences under isotopy.^[76] Additionally, far commutativity holds for non-adjacent generators:

\sigma_i \sigma_j = \sigma_j \sigma_i \quad \text{if} \quad |i - j| > 1,

ensuring that distant strands do not interfere.^[76] These relations suffice to define the group, as proven by Artin, who showed that any braid can be reduced to a canonical form using them.^[90] A representative example is the 3-braid group B_3, generated by \sigma_1 and \sigma_2 subject to the single braid relation \sigma_1 \sigma_2 \sigma_1 = \sigma_2 \sigma_1 \sigma_2. This group is isomorphic to the fundamental group of the complement of the trefoil knot in \mathbb{R}^3, highlighting connections between braids and knot complements.^[91] Regarding computability, the word problem in braid groups is solvable via algorithms that reduce words to unique normal forms, such as Garside's normal form, enabling efficient verification of equality between braid words despite the groups' infinite nature.^[92] In modern applications, braid groups facilitate path planning in robotics, where trajectories of multiple tethered or untethered agents are modeled as braids to ensure collision-free motions and detect entanglements in configuration spaces.^[93] Similarly, in cryptography, braid-based encryption protocols exploit the computational hardness of problems like the conjugacy search problem in B_n, proposing public-key systems resistant to classical attacks, though vulnerabilities have been identified in some schemes.^[94] These uses underscore the braid groups' utility beyond pure algebra, linking to practical computational challenges. In braid theory, these algebraic elements correspond geometrically to isotopy classes of strand diagrams in the plane.

Symbolism and Metaphors

Cultural Symbolism

In various African cultures, such as among the Himba people of Namibia, braided hairstyles serve as important indicators of social status, including marital status and age; for instance, unmarried girls typically wear two plaits (ozondato) hanging forward over their faces, while married women or new mothers adopt an Erembe headdress crafted from animal skin to signify their transition to adulthood and family roles.^[95]^[96]^[97] This practice underscores braids' role in communal identity and life stages, extending beyond aesthetics to encode personal and societal narratives. Among Native American traditions, sweetgrass braids hold profound spiritual significance in smudging ceremonies, where the plant—regarded as the sacred hair of Mother Earth—is braided, dried, and burned to purify spaces, attract positive energies, and symbolize healing, peace, and interconnectedness with the natural world across tribes like the Cree and Lakota.^[98]^[99] These braids, often consisting of three strands representing unity, are used in rituals to honor ancestors and foster harmony, highlighting braids as conduits for sacred communication.^[100] In Renaissance art, braided hair frequently conveyed layers of symbolism related to virtue, status, and sensuality; Sandro Botticelli's portraits, such as Portrait of a Young Woman, depict women with elaborate bound braids intertwined with pearls, signaling marital eligibility or wedded status while evoking erotic undertones as a "threshold to desire" in Florentine society.^[101]^[102] This artistic motif extended to modern tattoos, where braided designs—such as rope-like patterns—represent resilience, unity, and the strength to endure challenges, often chosen to embody personal empowerment and interconnected life journeys.^[103] Global indigenous traditions further illustrate braids' symbolic depth; in Māori culture, tā moko tattoos incorporate interlocking linear and spiral motifs symbolizing whakapapa (genealogy), cultural heritage, and prestige, as these chiseled designs narrate an individual's ancestry and societal role.^[104] The symbolism of braids has evolved historically from associations with fertility in ancient depictions—such as the stylized braided caps on Paleolithic Venus figurines like the Venus of Willendorf, interpreted as emblems of abundance and the divine feminine—to markers of empowerment in 20th-century movements; during the 1970s Black Power and feminist eras, Black women reclaimed cornrows and box braids as acts of cultural defiance and self-affirmation against Eurocentric beauty standards, transforming them into icons of racial pride and autonomy.^[4]^[105]^[106]^[107]

Literary and Idiomatic Uses

In English literature and idiom, the term "braid" has evolved from its etymological roots to embody themes of interlacing, complexity, and transformation. Originating from Old English bregdan, meaning "to move quickly, pull, shake, or weave," the word entered Middle English as breyden around the 14th century, shifting toward connotations of plaiting or twisting strands together. This Proto-Germanic base, akin to Old Norse bregða ("to draw or brandish"), initially carried senses of sudden action or deceit, as in a "braid" denoting a trick or stratagem by circa 1200. By the 19th century, poetic applications highlighted aesthetic and symbolic depth; for instance, Alfred Lord Tennyson's Locksley Hall (1842) evokes "a swarm of fire-flies tangled in a silver braid" to depict celestial beauty and entanglement, while W.S. Gilbert's lyric "Braid the Raven Hair" (1867) uses braiding as a metaphor for enhancing feminine allure through deliberate adornment.^[108]^[109]^[110]^[111] Idiomatic expressions extend "braid" into figurative realms, often symbolizing unity amid multiplicity or intricate pathways. The phrase "braided river," borrowed from geomorphology to describe rivers with interwoven channels, serves as a literary metaphor for meandering, resilient journeys; in Dorothy Tse's The Braided River: Migration and the Personal Essay (2019), it illustrates the nonlinear flow of migrant identities across cultures, emphasizing convergence and divergence in personal narratives. Similarly, "braided fates" evokes intertwined destinies, as in Karla M. Jay's historical novel When We Were Brave (2019), where it captures the linked lives of characters navigating World War II's upheavals, underscoring shared vulnerability and hope. These idioms draw briefly from cultural symbolism of braids as bonds but adapt them to verbal expressions of relational complexity.^[112]^[113] In literature, braids frequently represent identity, preparation, and narrative structure. Homer's Odyssey employs "lovely braids" (eukómōn) as an epithet for goddesses like Calypso, symbolizing divine elegance and otherworldly poise, as when she is described as "the nymph with lovely braids" in Book 5, highlighting her allure amid Odysseus's trials. Modern works amplify this for cultural identity; in Cherie Dimaline's The Marrow Thieves (2017), protagonist Frenchie's long braid signifies Indigenous pride and resilience against colonial erasure, embodying a tactile link to heritage and survival. The concept of "braided narratives" further illustrates structural metaphor, where stories interweave multiple threads for depth—exemplified in Jason Fagone's essay "The Jessica Simulation" (2020), which braids personal loss with AI ethics to explore emotional entanglement in contemporary nonfiction. Such uses prioritize conceptual unity over isolation, reflecting braids' enduring role in evoking cohesion in fragmented human experiences.^[114]

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Celtic Knots: Discover the Meaning Behind These Intricate Designs
Nov 15, 2020 · The first interlace patterns—looping, braiding, and knotting—arrived on the British Isles with the Romans in the third or fourth century CE. As ...
[29]
Points, Laces and Chapes : Historic Enterprises, We're Making History
14-day returnsA necessity of medieval male dress, these laces (also called 'points') are used to close a man's hose, and to secure the hose to his doublet ...Missing: Europe | Show results with:Europe
[30]
Middle Ages - epochs-of-fashion: Costume and Dress throughout ...
The clothing of medieval women was floor-long or ankle-long and had likewise long sleeves. All materials were made from natural fibres, such as hemp fibres ( ...
[31]
History of Friendship Bracelets by The Lanyard Ladies
Life Script suggests that the friendship bracelet is a direct descendant of Central American Indian crafts. The friendship bracelet first appeared in the U.S. ...Missing: modern | Show results with:modern
[32]
https://www.lanyardladies.com/history-of-friendship-bracelets
[33]
https://macramecordspari.com/blogs/discover-the-world-of-macrame-art/innovative-macrame-applications-in-fashion-and-accessories
[34]
The Invention of Rope: A Journey Through History
Aug 26, 2024 · In ancient Egypt, rope was made from water reeds and date palms, while in Mesopotamia, ropes were crafted from flax and hemp.
[35]
Introduction to Rope — Construction, Materials, Etc. | Art of Manliness
Jan 16, 2020 · Ropes are constructed in 2 primary ways: laid and braided. Laid Rope. Different parts of Rope illustration. Laid rope is also known as twisted ...
[36]
Rope Constructions - Marlow Ropes
Rope constructions include traditional twisted ropes (3-strand), single braids (8-strand), and cover constructions (8-plait, 16-plait over 2 under 2, 24-plait).
[37]
Rescue Rope and Cord Construction - Rigging Lab Academy
May 15, 2023 · Learn about rescue rope and cord construction, including kernmantle ropes, fiber comparisons, and rope manufacturing processes for technical rescue teams.Missing: methods plaited tensile
[38]
(PDF) About 75 years of synthetic fiber rope history - ResearchGate
Apr 16, 2022 · Nylon was discovered in the late 1930's and was first introduced into fiber ropes during World War II. Since that time a number of other ...
[39]
https://www.researchgate.net/publication/315918880_About_75_years_of_synthetic_fiber_rope_history
[40]
Nylon Ropes - Strengths - The Engineering ToolBox
Nylon 3-strand and 8-strand rope - minimum breaking strength and safe load. Nylon rope is made from continuous filament polyamide - nylon 6 or nylon 6.6.
[41]
Rope Twisted vs Braided Rope: Which One Should You Choose?
Sep 4, 2025 · The braided construction distributes load across many more fiber contact points than twisted rope, typically resulting in higher strength ...
[42]
Twisted Rope vs. Braided Rope - Seaco Industries
There is usually excellent flexibility with braided rope, while many twisted ropes feel stiff and can be hard to maneuver.
[43]
https://www.seacorope.com/blog/%25EF%25BF%25BCtwisted-rope-vs-braided-rope/
[44]
Foil Shielding vs. Braided Shielding in Cable Assemblies
Jul 3, 2024 · The most traditional form of shielding, braided shielding only provides 70-90 percent coverage, while foil shielding provides 100 percent. One ...Shielded Cable: Foil... · Types Of Shielded Cable · Braided Shielding
[45]
https://www.iconnsystems.com/blog/foil-shielding-vs.-braided-shielding-in-cable-assemblies
[46]
Coaxial Cable – 1929 - Magnet Academy - National MagLab
Espenschied and Affel filed a patent for coaxial cable in 1929, which was granted in 1931. The design was a great improvement over other types of wire available ...
[47]
Braided Wire Harnesses: Advantages & Applications | ETI
Apr 29, 2025 · Braiding in wire harness assembly isn't just for looks—it enhances durability and performance. Discover why our experts choose to braid our ...
[48]
A Quick Explanation of Shielding for Audio Cables and ... - Belram
Braided shielding, like its name suggests, is an interwoven set of thin tin or copper wires grouped together to protect the cable from electric interference.
[49]
How Braided Sleeving Benefits the Future of Automotive Applications
Braided sleeving is an ideal wire management tool because it maintains flexibility as it navigates a vehicle's complex structure.
[50]
Braiding & Shielding | EMI Shield, Special Purpose Cable, Custom ...
Braided shield: A wire braid is formed the same way as a textile braid, with an overlapping, interwoven pattern. Calmont can design the angle and density of ...
[51]
How Cables Are Made - Step 5: Braiding - HELUKABEL
Feb 16, 2022 · Braided screens, on the other hand, easily withstand bending and unbending cycles in drag chains and have about 85 percent coverage. Generally ...
[52]
[PDF] SHIELDED CABLES WITH OPTIMAL BRAIDED SHIELDS by ... - OSTI
Jan 24, 1991 · Large-angle braids thus require more copper and cost more to produce (because of the lower plaiting speed) than do those with small angles.Missing: overlap | Show results with:overlap
[53]
How to Braid Onions | Almanac.com
Oct 16, 2024 · Braiding onions instructions and pictures. Help your harvest last longer!
[54]
Braiding Onions and Garlic - The Italian Garden Project
Jul 20, 2020 · Braiding strands is just what you do after harvesting, at least with most varieties of onions and soft neck garlic.
[55]
Garlic Braiding - My Kitchen Wand
Aug 6, 2017 · Garlic braids were used in ancient Greece as a ward to protect babies and children against evil. The custom carried over to households and shops ...Missing: Mediterranean farming century
[56]
Braiding Red Garlic of Sulmona - Abruzzo With Gusto
Jul 15, 2017 · A braid of Sulmona red garlic is normally double, with 40-50 bulbs and weighs up to 3 kg. To see whether it was made by an expert, you have to look on the ...
[57]
https://abruzzowithgusto.com/braiding-red-garlic-sulmona/
[58]
Garlic Braids 18 in Information and Facts - Specialty Produce
The braids were used as food, medicinally, and spiritually by many different ancient cultures throughout history.
[59]
How to Braid Garlic and Onions - Abundant Permaculture
Oct 17, 2022 · Learn how to braid garlic and onions for long-term storage, including tips on curing and storing for the best results.Missing: symbols festivals<|control11|><|separator|>
[60]
Onion Braids: functional, symbolic, marketing ploy. - Turkeysong
Nov 10, 2013 · It is symbolic of something more tangible and close to home; something that is not just playing at a fantasy of real food and farm, so much as ...
[61]
🍞🌾🌻 Blessed Lughnasadh 🌾🍞🌻 Today marks ... - Facebook
Aug 1, 2025 · Make an onion or garlic braid to hang in your home for protection. Place a bouquet of sunflowers on your table to bring the brightness of ...
[62]
Weaving Strands of Challah History - Reform Judaism
Oct 30, 2012 · In medieval times, it was common throughout Eastern Europe to braid all types of baked goods. Jewish cooks, wanting to make their challot ...
[63]
Yesterdish's Challah
Aug 12, 2013 · Challah as we know it emerged in in the late 14th or early 15th century in Eastern Europe, most likely from Vienna, where it shares a common origin with ...
[64]
The challah represents unity - Jewish Independent
Nov 3, 2017 · The challah braid represents the unity of everything. It ties all the physical properties of our lives to the divine. Similarly, Shabbat uplifts ...Missing: symbolic | Show results with:symbolic
[65]
Why Rosh Hashanah Challah Is Round, Not Braided - Chabad.org
The braided challah is the symbol of this unity. Separate strands twist tightly together to form a picture-perfect whole, the ideal shape with which to ...
[66]
Braid Challah Like a Pro with This Step-by-Step Guide - The Kitchn
Nov 22, 2021 · Divide the dough into four even pieces, then roll out each piece of dough into strands that are even in length and width, slightly tapering the ...
[67]
Challah Part 2: How to Braid Challah - Tori Avey
Rating 5.0 (16) · 4 hr 45 minPinch the ends of the loose strands together and tuck both the top and bottom tips of the challah under to create a nice rounded shape.
[68]
3 Stunning Ways to Shape Brioche - The Kitchn
Jul 30, 2019 · When you reach the end of the strands, tightly pinch together the ends to lock the shape into place. 4. Gently transfer the braid to a pain ...
[69]
Tender Braided Brioche Bread - SueBee Homemaker
Rating 4.6 (9) · 2 hr 25 minDec 16, 2023 · The bread dough divided in half. ... Place all three rolls together on top and then braid the strands together, tucking the ends underneath.
[70]
Bread scoring patterns and techniques | King Arthur Baking
Oct 20, 2017 · The curve helps create a lip at each cut that peels back when the dough is baked. Start at the side farthest from you and make an angled cut to ...Missing: benefits braiding
[71]
How to Braid Bread: A Step-by-Step Guide - Taste of Home
Aug 20, 2025 · First, braiding bread offers essential structural support to the loaves. Enriched dough is soft and tender due to its high fat content, which ...
[72]
https://www.tasteofhome.com/article/how-to-braid-bread/
[73]
Soft and Fluffy Braided Italian Bread: The Traditional Recipe
1 minKnead dough, let it rise, divide into strands, braid, cut ends, brush with egg, let rise again, then bake at 350°F for 40 minutes.
[74]
Swedish limpa bread - Caroline's Cooking
Rating 5.0 (3) · 1 hrNov 6, 2023 · Swedish limpa bread is a wonderfully soft part rye loaf with a touch of spice and molasses. Easy to make & delicious with simple toppings.
[75]
[PDF] Theory of Braids
Jun 22, 2013 · A theory of braids leading to a classification was given in my paper "Theorie der Zopfe" in vol. 4 of the Hamburger Abhandlungen (quoted as ...
[76]
[PDF] An Introduction to Braid Theory - Maurice Chiodo
Nov 4, 2005 · The theory of braids has been studied since the early 1920's, founded by Emil. Artin, a German mathematician (see [1], which is his original ...
[77]
[PDF] Introduction to Braid Groups - UChicago Math
ABSTRACT. This paper is an introduction to the braid groups in- tended to familiarize the reader with the basic definitions of these mathematical objects.
[78]
[PDF] Basic results on braid groups - Numdam
The term braid group was used for the first time by Emil Artin in 1925 [2], although probably these groups were considered for the first time by Hur- witz ...<|separator|>
[79]
Braid Groups: A Survey | SpringerLink
The terms “braid” and “braid groups” were coined by Artin, 1925. In his paper, an n-braid appears as a specific topological object. We consider two parallel ...Missing: original | Show results with:original
[80]
the case study of the braid group between 1925 and 1950
Oct 17, 2018 · Artin's paper is considered the first introduction to braid because of his explicit way of studying braids [2,3,4,27] which was to arithmetize ...
[81]
[PDF] Knots and braids - ICTP
Alexander theorem (1923): Every oriented knot or link may be isotoped to a closed braid. The Alexander theorem. Proof 1 (Alexander, 1923): The braid axis is ...
[82]
[PDF] Knots to Braids - UChicago Math
Aug 26, 2011 · Theorem 5.1. (Markov) The closures of two braids B and B0 represent the knot or link L if and only if one braid can be deformed into the other ...
[83]
[PDF] Braid Groups
Apr 17, 2016 · Introduction. Braid groups were introduced by Emil Artin in 1925, and by now play a role in various parts of mathematics including knot theory, ...
[84]
[PDF] Synergistic Coordination of Chromatin Torsional Mechanics and ...
Oct 17, 2019 · DNA replication in eukaryotes generates DNA super- coiling, which may intertwine (braid) daughter chro- matin fibers to form precatenanes, ...
[85]
Physicists take step toward fault-tolerant quantum computing
Apr 12, 2023 · This process of exchange is called a braid, after the shapes of the particle trails. “Quantum mechanically, when you move one particle ...Missing: mechanics | Show results with:mechanics
[86]
[PDF] Braiding, Majorana Fermions, Fibonacci Particles and Topological ...
Such particles are called Anyons. The braiding in these models is related to topological quantum field theory. Topological quantum computing.
[87]
[PDF] EDWARD FADELL' and LEE NEUWIRTH
In the first part of this paper we give the fundamental sequence of fibrations for the study of configuration spaces, and localize the problem ... Neuwirth, The ...
[88]
[PDF] EDWARD FADELL¹ and LEE NEUWIRTH
In the first part of this paper we give the fundamental sequence of fibrations for the study of configuration spaces, and localize the problem ... Neuwirth, The ...Missing: PDF | Show results with:PDF
[89]
Braid group:B3 - Groupprops
Dec 18, 2010 · Up to isomorphism, it is also equivalent to the following: The knot group of the trefoil knot. The universal central extension of special ...
[90]
A New Algorithm for Solving the Word Problem in Braid Groups
Our algorithm, although not better in complexity, is faster in comparison with known algorithms for short braid words, and it is almost independent of the ...Missing: computability | Show results with:computability
[91]
[PDF] CONFIGURATION SPACES, BRAIDS, AND ROBOTICS - Penn Math
The n-strand braid group of a space X is defined to be Bn(X) := π1(UCn(X)), whereas the n-strand pure braid group of X is Pn := π1(Cn(X)).
[92]
[0711.3941] Braid Group Cryptography - arXiv
Nov 26, 2007 · A number of public key cryptosystems based on com- binatorial group theoretic problems in braid groups have been proposed. We survey these cryptosystems.
[93]
[PDF] The Hair Salon as Contact Zone - UC San Diego
Nov 3, 2013 · Married women and new mothers wear Erembe headdresses made from animal skin. Similarly, men wear a single braid to indicate their single status.
[94]
Chapter 4.4 Art in Nomadic Societies – The Bright Continent
This Himba woman's hair is wrapped with leather, and its crest is made ... Women's hairstyles reflected marital status. By the late nineteenth century ...
[95]
Native American Uses for Sweetgrass - NativeTech
Many Native tribes in North America use sweetgrass in prayer, smudging or purifying ceremonies and consider it a sacred plant. It is usually braided, dried, and ...
[96]
Four Sacred Medicines | American Indian Health Service of Chicago ...
Sweetgrass is the sacred hair of mother earth. It can be used as a purifying herb, as incense in smudging. Herbal tea made from the leaves has been used to ...
[97]
Portraits and fashion: Sandro Botticelli, Portrait of a Young Woman
Her bound-up hair, for example, was a typical hairstyle for married women (unmarried women commonly wore their hair down).
[98]
The Renaissance Lets Its Hair Down - JSTOR Daily
Jan 10, 2023 · Sandro Botticelli emerged as the great painter of hair, making it what Lugli calls the “threshold to erotic desire” for spectators.
[99]
The Art of Rope Tattoo: Symbolism Unveiled - Artistic Innovators
A tattoo featuring a thick, braided rope can symbolize a person's ability to withstand life's challenges and emerge stronger. It can also represent the idea of ...
[100]
Art of the South Pacific: Polynesia - Art History Teaching Resources
Both men and women are tattooed with designs that are meaningful to the individual, and the art is associated with prestige, societal rank and status, and ...
[101]
Ancient Hairstyles of the Greco-Roman World
Dec 9, 2015 · ... braid. ... These might be linked to worship of the Great Goddess of Cyprus, an ancient fertility deity who became assimilated with Aphrodite.
[102]
How Natural Black Hair at Work Became a Civil Rights Issue
Jul 3, 2019 · The “Black Is Beautiful” movement assured black women and men that their skin, facial features, and natural hair were admirable—as is. The ...Missing: feminist | Show results with:feminist
[103]
Braid - Etymology, Origin & Meaning
Originating c. 1200 from Old English bregdan, meaning "move quickly, weave, knit," braid means to twist or plait hair and also refers to a trick or ...
[104]
braid, v.¹ meanings, etymology and more | Oxford English Dictionary
The earliest known use of the verb braid is in the Old English period (pre-1150). It is also recorded as a noun from the Old English period (pre-1150).
[105]
Locksley Hall | The Poetry Foundation
Many a night I saw the Pleiads, rising thro' the mellow shade,. Glitter like a swarm of fire-flies tangled in a silver braid. Here about the beach I wander' ...
[106]
Braid the Raven Hair by William Schwenck Gilbert - All Poetry
Braid the raven hair, Weave the supple tress, Deck the maiden fair. In her loveliness; Paint the pretty face, Dye the coral lip, Emphasise the grace
[107]
The Braided River: Migration and the Personal Essay ... - Amazon.com
I loved how the author used the metaphor of the braided river to demonstrate how we are all intertwined although cultures may be different, we all came from ...
[108]
When We Were Brave: Amazon.co.uk: Jay, Karla M
Rating 4.6 (3,346) ... braided fates we pray will work out in the end.' Rich in detail and obviously well-researched, this is one of the finest WW II novels that bears witness to ...Missing: literature | Show results with:literature
[109]
Braids Symbol Analysis - The Marrow Thieves - LitCharts
Jul 15, 2019 · For Frenchie, his long braid is a source of pride. As far as he's concerned, it signifies his identity as an Indigenous person and within the safety of his ...