Ir al contenido (pulsa Retorno)

Universitat Politècnica de Catalunya

    • Català
    • Castellano
    • English
    • LoginRegisterLog in (no UPC users)
  • mailContact Us
  • world English 
    • Català
    • Castellano
    • English
  • userLogin   
      LoginRegisterLog in (no UPC users)

UPCommons. Global access to UPC knowledge

13.363 Articles in journals published by the UPC
You are here:
View Item 
  •   DSpace Home
  • Revistes
  • Structural topology
  • 1993 núm 20
  • View Item
  •   DSpace Home
  • Revistes
  • Structural topology
  • 1993 núm 20
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Tilings, quasicrystals, and Hilbert's 18th problem

Thumbnail
View/Open
st20-05-a1-ocr.pdf (5,955Mb)
Share:
 
  View Usage Statistics
Cita com:
hdl:2099/1088

Show full item record
Senechal, Marjorie
Document typeArticle
Defense date1993
PublisherUniversité du Québec à Montréal
Rights accessOpen Access
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder
Abstract
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.
CitationSenechal, Marjorie. "Tilings, quasicrystals, and Hilbert's 18th problem". Structural Topology, 1993, núm. 20 
URIhttp://hdl.handle.net/2099/1088
ISSN0226-9171
Collections
  • Structural topology - 1993 núm 20 [8]
Share:
 
  View Usage Statistics

Show full item record

FilesDescriptionSizeFormatView
st20-05-a1-ocr.pdf5,955MbPDFView/Open

Browse

This CollectionBy Issue DateAuthorsOther contributionsTitlesSubjectsThis repositoryCommunities & CollectionsBy Issue DateAuthorsOther contributionsTitlesSubjects

© UPC Obrir en finestra nova . Servei de Biblioteques, Publicacions i Arxius

info.biblioteques@upc.edu

  • About This Repository
  • Contact Us
  • Send Feedback
  • Inici de la pàgina