Satin Weave Geometry and Move Number
topic
Satin weave construction requires a repeat size n with move number m where m and n share no common factors other than 1, with 5-shaft satin using move number 2 or 3, 8-shaft satin using move number 3 or 5, and 12-shaft satin using move numbers 5 or 7, with the move number determining the angular position of the binding point progression that distributes binding points maximally around the repeat to avoid diagonal grouping that would create twill-like lines disrupting the smooth surface.
Role
Defines the mathematical foundation of satin weave construction through the number-theoretic requirement that prevents binding point clustering, with understanding the move number constraint being essential for constructing valid satin weaves at any repeat size and for explaining why not all repeat sizes and move number combinations produce the characteristically smooth satin surface that requires maximum binding point separation in the repeat.