What is it? Considering braid technique and structure.

MATEC Web of Conferences

The role of the braid group constitutes one of the invariant measurements. Through the classification of braids formed several parts of the braid group, but does not computationally distinguish them. Some characteristics have been expressed to give the features to a braid in braid group based on redefining relation between braid group and permutation group.

We introduce braids via their historical roots and uses, make connections with knot theory and present the mathematical theory of braids through the braid group. Several basic mathematical properties of braids are explored and equivalence problems under several conditions defined and partly solved. The connection with knots is spelled out in detail and translation methods are presented. Finally a number of applications of braid theory are given. The presentation is pedagogical and principally aimed at interested readers from different fields of mathematics and natural science. The discussions are as self-contained as can be expected within the space limits and require very little previous mathematical knowledge. Literature references are given throughout to the original papers and to overview sources where more can be learned.

Australian Journal of Clinical Hypnotherapy and Hypnosis, 2018

The ‘boundary-work’ activities of James Braid (1795-1860), natural philosopher, gentleman scientist, structured thinker, and well-respected Manchester surgeon were unexpectedly reactivated in late 1859 by the sudden Continental interest in the use of his techniques for inducing hypnotic anaesthesia. This article examines Braid’s immediate response to that interest and, also, provides details of the matters Braid addressed in his last three letters, written just weeks before his death. In addition to his considerable contributions to surgery and medicine, a strong case is made for the unparalleled watershed importance of Braid and his discoveries, his theoretical understandings, his therapeutic innovations, and his relentless ‘boundary-work’ in relation to the establishment of hypnotism as an appropriate, entirely autonomous domain of philosophical and medico-scientific inquiry; and, in doing so, an appraisal is made of Braid’s true significance, his clear priority, his continued disciplinary relevance, and his undoubted pre-eminence in the domain of ‘psycho-physiology’.

The salt mine at Hallstatt in Austria is known for its rich organic finds from the middle Bronze (1600-1200 BC) and early Iron Age (Hallstatt Period, c. 800-400 BC), including wood, fur, leather, tree bast and textiles. Hallstatt presents a unique situation, and the textiles found there allow us to study in detail the development of textile technology in the period from 1500 to 400 BC. Among the narrow fabrics there are two fragments which were made using braiding techniques. In the present article, we will discuss different braiding techniques and explore the possibility of tracing the fragments back to an early version of loop braiding.

2015

The fishtail braid, newly popular in the past five years on adult women on New York streets and the runway, also conspicuously adorns the famed Caryatids, or maidens, 430 BCE, from the Erechtheion on the Athenian Acropolis. The Caryatids have been carefully studied for their pose and clothing, but their unique hairstyles have been overlooked. Previous scholars described these ancient hairstyles simply as braided without defining the specific braids used or whether or not the hairstyle could be recreated. No one had identified the fishtail braid as the main braid down the back and as the style of some of the side braids wrapped around the heads of the Caryatids. The authors worked with a professional hairstylist and six Fairfield University student models to demonstrate that these ancient Greek arrangements of braids were not merely the creations of sculptors but could have been worn. Our project recreating the braids and their arrangements is a research method known as experimental ...

Catwalk: The Journal of Fashion, Beauty, and Style , 2015

The fishtail braid, newly popular in the past five years on adult women on New York streets and the runway, also conspicuously adorns the famed Caryatids, or maidens, 430 BCE, from the Erechtheion on the Athenian Acropolis. The Caryatids have been carefully studied for their pose and clothing, but their unique hairstyles have been overlooked. Previous scholars described these ancient hairstyles simply as braided without defining the specific braids used or whether or not the hairstyle could be recreated. No one had identified the fishtail braid as the main braid down the back and as the style of some of the side braids wrapped around the heads of the Caryatids. The authors worked with a professional hairstylist and six Fairfield University student models to demonstrate that these ancient Greek arrangements of braids were not merely the creations of sculptors but could have been worn. Our project recreating the braids and their arrangements is a research method known as experimental archaeology, a way to test hypotheses related to antiquity by using methods as archaeologically accurate as possible, and striving for historically accurate results. The project’s genesis began in 2007 with the exhibition The Creative Photograph in Archaeology at Fairfield University, in which detailed photographs of the Caryatids provided uncommon views of their hair. In 2009, Professor of Art History Katherine A. Schwab made an internationally-screened short film which provides the basis for further inquiry on technique and meaning. Coincidentally, at the same time, the fishtail braid began to be featured prominently on runways and in the fashion press. This article examines the techniques and meanings of the fishtail braid, which connect girls and women today to their counterparts in antiquity. Students who wore the braids thought about hairstyles in an entirely new way and as a compelling portal to another time and place. Ancient Athenians were no longer a vague concept but real people whose lives were played out in the surviving art.

Journal of Textile and Apparel Technology and Management, 2012

The paper describes a study which identified how various yarns, their corresponding spool placement, and interlacements affected the structure, appearance, and shape of a tubular braid. By replacing one certain element or variable of the braid structure with a differing variable, (i.e. color, fiber, spool placement, or interlacement structure), a variance is created, in a similar way to the creation of special effects in a fancy yarn. Though there were several machines available for braid production, the Cobra 450 Maypole braider was chosen to fabricate the experimental products due to its ease of operation, manipulation, and spool replacement. This unit produced hollow braids that allowed the structure to be utilized with or without a core; the machine was also capable of fabricating flat braids through the depression of the tubular structure and stitching the braid flatly in place. By producing a series of braids, an improved comprehension of machine settings, material choice, and placement of yarns was achieved, while simultaneously fabricating a heightened design aesthetic in producing visual effects. Experimental design studies within the preliminary work included color pattern development and structural effects. Imagery of the variety of designs produced is included along with an analysis of all braid designs.

This article concerns hair samples collected in 1925 in the Ojibwe community of Red Lake, Minnesota, USA, now in the collections of the Pitt Rivers Museum, Oxford. It outlines the process of consultation with community members and of the discovery of the historical context and meanings surrounding the hair. These meanings are emotive because of the conjuncture of Ojibwe beliefs about hair with the history of the cutting and analysis of hair by Whites as part of attempts to control Ojibwe people in various ways. The article also explores the implications of current theory about material culture which sees artefacts as points of contact between peoples, and which focuses on tracing the movements and shifting meanings of artefacts as a way of understanding the relations between the peoples involved.

Fornvännen (Journal of Swedish Antiquarian Research), 2013

The Historical Museum in Stockholm holds two interesting Medieval braids, one from Riddarholmen Church and one from Alvastra Abbey. Both are made of red silk and metal thread, probably with a loop-manipulation braiding technique that can produce openwork braids resembling lace. The braid from Riddarholmen can be linked to funerary textiles, as it was found during the opening in 1915–16 of the purported tomb of King Magnus Birgersson Ladulås (Barnlock). The other braid was excavated in 1949 at Alvastra Abbey and is probably a fastening loop. In this study, we present the results of a technical and material comparison of the two braids.

Fundamenta Mathematicae, 2004

This paper gives a new method for converting virtual knots and links to virtual braids. Indeed, the braiding method given here is quite general and applies to all the categories in which braiding can be accomplished. This includes the braiding of classical, virtual, flat, welded, unrestricted, and singular knots and links. We also give reduced presentations for the virtual braid group and for the flat virtual braid group (as well as for other categories). These reduced presentations are based on the fact that these virtual braid groups for n strands are generated by a single braiding element plus the generators of the symmetric group on n letters.