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The Strength of a Fabric
Author(s) -
Clapham C. R. J.
Publication year - 1994
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/26.2.127
Subject(s) - hang , mathematics , measure (data warehouse) , breaking strength , composite material , structural engineering , computer science , materials science , engineering , database
Consider fabrics in which every warp (and weft) strand passes over and under at least k weft (warp) strands. There is a 4 k by 4 k fabric of this kind that does not hang together. We prove that any n by n fabric of this kind, where n < 4 k , does hang together. Moreover, we introduce a measure of how well a fabric hangs together, by defining the strength of a fabric, and two theorems are proved that extend the preceding results.