Les pavages, les quasi-cristaux et le 18th problème de Hilbert

Le 18e problème de Hilbert est constitué de trois questions vaguement liées : Le nombre de groupes a région fondamentale (bornée) dans E mest-il fini ? Existet-il un pavage sur les paves duquel aucun groupe n’agisse de façon transitive ? Quels sont les juxtapositions les plus denses de corps congruents dans E3 ? Ces questions ont orienté la cristallographie mathématique vers de nouvell es directions et ont été excessivement efficaces: de nos jours, les quasicristaux posent des problèmes mathématiques qui se situent précisément dans les champs indiqués par Hilbert. En effet, plusieurs des nouveaux problèmes sont des reformulations de ceux de Hilbert. On a fait de considérables progrès dans les demières années, mais une question clé - comment les parties du problème sont liées entre elles - n’e st pas encore complètement comprise.Hilbert’s 18th problem consisted of three loosely related questions: Is the number of groups in En with (bounded) fundamental region finite? Does there exist a tiling on whose tiles no group acts transitively? What are the densest packings of congruent bodies in E3? These questions pointed mathematical crystallography in new directions and have been unreasonably effective: in our time quasicrystals pose mathematical problems in precisely the areas indicated by Hilbert. Indeed, many of the new problems are reformulations of Hilbert’s. Considerable progress has been made in the last few years, but a key issue-how the parts of the problem are related to one another-is still not completely understood.Peer Reviewe

Book Review: It Walks in Beauty: Selected Prose of Chandler Davis, Edited and with an Introduction by Josh Lukin

To paraphrase William Butler Yeats (with apologies), how can we knowthe edited from the editor

Preface

Silk Roads, Other Roads, the Eighth Biennial Symposium of the Textile Society of America, was held September 26-28, 2002 at Smith College in Northampton, Massachusetts. Anthropologists, archeologists, artists, art historians, conservators, curators, designers, historians, and other professionals contributed to the rich and varied program featuring silk and other textiles around the world and through time. Topics included archaeology along the silk road; textile artisans and sustainable development; textiles along the spice routes; acculturation; silk in medieval Europe; silk production in mainland Southeast Asia; the American silk industry and, more generally, its textile industry; Andean textiles; silk traditions in Japan; new directions in silk fabric design; trade in Asia. This Proceedings, the first in the TSA Symposium series to appear on CD ROM, contains the texts of these juried presentations. The TSA 2002 Symposium also featured a keynote lecture each day (not included here): Francesca Bray, Professor of Anthropology at the University of California at Santa Barbara, on “Womanly Work: ideals and realities of textile production in Imperial China,” Daryl Hafter, Professor of History at Eastern Michigan University and President of the Society for the History of Technology, on “Women, Cloth & Politics in Lyon’s Eighteenth-Century Silk Industry,” and members of the Northampton Silk Project Steering Committee on their town-wide six-year study of Northampton\u27s silk industry. The Symposium\u27s opening reception, held at Historic Northampton in conjunction with the opening of an exhibition of its silk costume collection, was followed by a Gallery Walk through town that introduced Symposium participants to Northampton’s many galleries, shops, and restaurants. Participants also enjoyed several other exhibitions related to the Symposium: new directions in silk fabrics, images of silk and silk production in rare books, rare handwoven Burmese silks (and a Burmese loom), and restored photographs of Northampton\u27s Nonotuck Silk Company. Pre-conference and post-conference tours included the Hancock Shaker Village, the Clark Institute in Williamstown, the Athenaeum in Hartford, the Textile History Museum in Lowell, the Boston Museum of Fine Arts, the Mead Museum at Amherst College, the Museum of Fine Arts in Springfield, Northampton\u27s historic silk sites, and a nearby fiber farm. It is a pleasure to thank Marilyn Smith, the Northampton Silk Project coordinator and this Symposium\u27s sine qua non, and our tireless Symposium committee members, Ute Bargmann, Diane Fagan-Affleck, Joan Hastings, Karen Herbaugh, Linda McIntosh, and Kiki Smith. Barbara Blumenthal organized and ran a very popular three-day Book Fair, and Amelia Hough-Ross ably assisted with the preparation of these Proceedings

Une introduction a la thkorie des figures: la géometrie de E.S. Fedorov

Peer Reviewe

Bounds for the Regularity Radius of Delone Sets

Delone sets are discrete point sets X in Rd characterized by parameters (r,R), where (usually) 2r is the smallest inter-point distance of X, and R is the radius of a largest ``empty ball that can be inserted into the interstices of X. The regularity radius ρ^d is defined as the smallest positive number ρ such that each Delone set with congruent clusters of radius ρ is a regular system, that is, a point orbit under a crystallographic group. We discuss two conjectures on the growth behavior of the regularity radius. Our ``Weak Conjecture states that ρ^d=O(d2logd)R as d→∞, independent of~r. This is verified in the paper for two important subfamilies of Delone sets: those with full-dimensional clusters of radius 2r and those with full-dimensional sets of d-reachable points. We also offer support for the plausibility of a ``Strong Conjecture , stating that ρ^d=O(dlogd)R as d→∞, independent of r. Delone sets are discrete point sets X in Rd characterized by parameters (r,R), where (usually) 2r is the smallest inter-point distance of X, and R is the radius of a largest ``empty ball that can be inserted into the interstices of X. The regularity radius ρ^d is defined as the smallest positive number ρ such that each Delone set with congruent clusters of radius ρ is a regular system, that is, a point orbit under a crystallographic group. We discuss two conjectures on the growth behavior of the regularity radius. Our ``Weak Conjecture states that ρ^d=O(d2logd)R as d→∞, independent of~r. This is verified in the paper for two important subfamilies of Delone sets: those with full-dimensional clusters of radius 2r and those with full-dimensional sets of d-reachable points. We also offer support for the plausibility of a ``Strong Conjecture , stating that ρ^d=O(dlogd)R as d→∞, independent of r

The Invention of Machine Twist \u3ci\u3ethe Nonotuck Silk Company, from moths to millions\u3c/i\u3e

Introduction. Cocoons and raw silk; thrown silk and dyed silk; spun silk yarns and fabrics; plain woven silks; lutestrings, sarsenets, satins, serges, foulards, tissues for hat and millinery purposes; figured silk piece goods, woven or printed, upholstery silks; crapes, velvets, gauzes; cravats, handkerchiefs, hosiery, knit goods, laces, scarves, ties, veils, all descriptions of cut and made-up silks; ribbons, plan fancy, and velvet; bindings, braids, cords, galloons, ladies\u27 dress trimmings, upholsters\u27, tailors\u27, military and miscellaneous; machines for the manufacture of silk goods: the American silk industry\u27s proud display had the post of honor at the east end of the Main Building, on the central aisle at the 1876 Centennial International Exposition in Philadelphia. The industry had burgeoned after the Civil War: only four of the thirty four silk exhibitors (representing America\u27s two hundred twenty four silk manufacturers and dealers) could trace their origins to the times which tried the souls of the silk producers and manufacturers. The Nonotuck Silk Company, the unlikely descendant of the 1830\u27s moth-to-cloth Northampton Silk Company, was one that could and did. After falling twice from the rickety carousel of early nineteenth century enterprises, it seized the brass ring and held on. The key to its success was its manufacture of the first usable machine twist, a silk thread strong and smooth enough to withstand the unprecedented demands of the newly invented sewing machine. Nonotuck became one of the nation\u27s leading silk thread manufactures and Northampton\u27s largest employer for decades. Yet the details of this key invention have never been spelled out. This paper attempts to fill that gap. The sericulture years: 1830 - 1850. The story begins, not in 1838 as the trade card suggests, but eight years earlier, when Samuel Whitmarsh, a 30-year-old Boston native, bought a large estate near the center of Northampton with the proceeds of a successful tailoring business in New York and built cocoonery for two million silkworms and two greenhouses for mulberry shoots next to his mansion. Raising silkworm was a popular spring pastime in Northampton in the 1820\u27s; Whitmarsh tugged the silkworm from cottage to factory, from hobby to industry. A former linseed oil mill three miles three miles to the north along the Mill River served as his first factory. A few years later, backed by a group of New York and Connecticut financiers, Whitmarsh built a four-story brick one nearby. The new7 factory hummed with up-to-the-minute machinery. Tourists flocked to see his power loom churn out silk ribbons and vesting. The Northampton Silk Company was incorporated in 1838. But some whispered that the manufacture was mostly a show to persuade the gullible to invest in mulberry trees, whose price increased tenfold in a few short years. The Northampton Silk Company burst with the mulberry bubble. Bankrupt, Whitmarsh withdrew in 1840. Out but not down, he tried, again unsuccessfully, to establish a silk industry in Jamaica a few years later. At the time of his death, in Northampton in 1875, he was planning to raise silk in California

The Invention of Machine Twist: the Nonotuck Silk Company, from moths to millions

Introduction. Cocoons and raw silk; thrown silk and dyed silk; spun silk yarns and fabrics; plain woven silks; lutestrings, sarsenets, satins, serges, foulards, tissues for hat and millinery purposes; figured silk piece goods, woven or printed, upholstery silks; crapes, velvets, gauzes; cravats, handkerchiefs, hosiery, knit goods, laces, scarves, ties, veils, all descriptions of cut and made-up silks; ribbons, plan fancy, and velvet; bindings, braids, cords, galloons, ladies\u27 dress trimmings, upholsters\u27, tailors\u27, military and miscellaneous; machines for the manufacture of silk goods: the American silk industry\u27s proud display had the post of honor at the east end of the Main Building, on the central aisle at the 1876 Centennial International Exposition in Philadelphia. The industry had burgeoned after the Civil War: only four of the thirty four silk exhibitors (representing America\u27s two hundred twenty four silk manufacturers and dealers) could trace their origins to the times which tried the souls of the silk producers and manufacturers. The Nonotuck Silk Company, the unlikely descendant of the 1830\u27s moth-to-cloth Northampton Silk Company, was one that could and did. After falling twice from the rickety carousel of early nineteenth century enterprises, it seized the brass ring and held on. The key to its success was its manufacture of the first usable machine twist, a silk thread strong and smooth enough to withstand the unprecedented demands of the newly invented sewing machine. Nonotuck became one of the nation\u27s leading silk thread manufactures and Northampton\u27s largest employer for decades. Yet the details of this key invention have never been spelled out. This paper attempts to fill that gap. The sericulture years: 1830 - 1850. The story begins, not in 1838 as the trade card suggests, but eight years earlier, when Samuel Whitmarsh, a 30-year-old Boston native, bought a large estate near the center of Northampton with the proceeds of a successful tailoring business in New York and built cocoonery for two million silkworms and two greenhouses for mulberry shoots next to his mansion. Raising silkworm was a popular spring pastime in Northampton in the 1820\u27s; Whitmarsh tugged the silkworm from cottage to factory, from hobby to industry. A former linseed oil mill three miles three miles to the north along the Mill River served as his first factory. A few years later, backed by a group of New York and Connecticut financiers, Whitmarsh built a four-story brick one nearby. The new factory hummed with up-to-the-minute machinery. Tourists flocked to see his power loom churn out silk ribbons and vesting. The Northampton Silk Company was incorporated in 1838. But some whispered that the manufacture was mostly a show to persuade the gullible to invest in mulberry trees, whose price increased tenfold in a few short years. The Northampton Silk Company burst with the mulberry bubble. Bankrupt, Whitmarsh withdrew in 1840. Out but not down, he tried, again unsuccessfully, to establish a silk industry in Jamaica a few years later. At the time of his death, in Northampton in 1875, he was planning to raise silk in California

Preface

Silk Roads, Other Roads, the Eighth Biennial Symposium of the Textile Society of America, was held September 26-28, 2002 at Smith College in Northampton, Massachusetts. Anthropologists, archeologists, artists, art historians, conservators, curators, designers, historians, and other professionals contributed to the rich and varied program featuring silk and other textiles around the world and through time. Topics included archaeology along the silk road; textile artisans and sustainable development; textiles along the spice routes; acculturation; silk in medieval Europe; silk production in mainland Southeast Asia; the American silk industry and, more generally, its textile industry; Andean textiles; silk traditions in Japan; new directions in silk fabric design; trade in Asia. This Proceedings, the first in the TSA Symposium series to appear on CD ROM, contains the texts of these juried presentations. The TSA 2002 Symposium also featured a keynote lecture each day (not included here): Francesca Bray, Professor of Anthropology at the University of California at Santa Barbara, on “Womanly Work: ideals and realities of textile production in Imperial China,” Daryl Hafter, Professor of History at Eastern Michigan University and President of the Society for the History of Technology, on “Women, Cloth & Politics in Lyon’s Eighteenth-Century Silk Industry,” and members of the Northampton Silk Project Steering Committee on their town-wide six-year study of Northampton\u27s silk industry. The Symposium\u27s opening reception, held at Historic Northampton in conjunction with the opening of an exhibition of its silk costume collection, was followed by a Gallery Walk through town that introduced Symposium participants to Northampton’s many galleries, shops, and restaurants. Participants also enjoyed several other exhibitions related to the Symposium: new directions in silk fabrics, images of silk and silk production in rare books, rare handwoven Burmese silks (and a Burmese loom), and restored photographs of Northampton\u27s Nonotuck Silk Company. Pre-conference and post-conference tours included the Hancock Shaker Village, the Clark Institute in Williamstown, the Athenaeum in Hartford, the Textile History Museum in Lowell, the Boston Museum of Fine Arts, the Mead Museum at Amherst College, the Museum of Fine Arts in Springfield, Northampton\u27s historic silk sites, and a nearby fiber farm. It is a pleasure to thank Marilyn Smith, the Northampton Silk Project coordinator and this Symposium\u27s sine qua non, and our tireless Symposium committee members, Ute Bargmann, Diane Fagan-Affleck, Joan Hastings, Karen Herbaugh, Linda McIntosh, and Kiki Smith. Barbara Blumenthal organized and ran a very popular three-day Book Fair, and Amelia Hough-Ross ably assisted with the preparation of these Proceedings

Les pavages, les quasi-cristaux et le 18th problème de Hilbert

Le 18e problème de Hilbert est constitué de trois questions vaguement liées : Le nombre de groupes a région fondamentale (bornée) dans E mest-il fini ? Existet-il un pavage sur les paves duquel aucun groupe n’agisse de façon transitive ? Quels sont les juxtapositions les plus denses de corps congruents dans E3 ? Ces questions ont orienté la cristallographie mathématique vers de nouvell es directions et ont été excessivement efficaces: de nos jours, les quasicristaux posent des problèmes mathématiques qui se situent précisément dans les champs indiqués par Hilbert. En effet, plusieurs des nouveaux problèmes sont des reformulations de ceux de Hilbert. On a fait de considérables progrès dans les demières années, mais une question clé - comment les parties du problème sont liées entre elles - n’e st pas encore complètement comprise.Hilbert’s 18th problem consisted of three loosely related questions: Is the number of groups in En with (bounded) fundamental region finite? Does there exist a tiling on whose tiles no group acts transitively? What are the densest packings of congruent bodies in E3? These questions pointed mathematical crystallography in new directions and have been unreasonably effective: in our time quasicrystals pose mathematical problems in precisely the areas indicated by Hilbert. Indeed, many of the new problems are reformulations of Hilbert’s. Considerable progress has been made in the last few years, but a key issue-how the parts of the problem are related to one another-is still not completely understood.Peer Reviewe