抄録
The study is to express some properties of satin weaves as function of numbers of one repeat n and counts a.
1) The relation between weft count a and warp count b is expressed as ab≡1 (mod n). (see eq. 1)
2) a-count satin and its complementary satin, ie (n-a)-count satin are in relation of mirror image. (see Fig. I)
3) When n is even and a<n/2-1, the weave in which the satin is put on itself, moving its origin by n/2 along weft way, becomes n/2 harness and a-count satin.
4) When a(n-a)≡1 (mod n) or a+b=n the adjacent 4 weave points on the design of this satin make square nets, which is called “squre type satin“.
5) When integers p and q which give satisfaction to following equation (eq. 5) exist, adjacent weave points make rectangular nets. (rectangular type satins)
6) When a2-1=n, the adjacent 4 weave points make lozenge nets. (lozenge type satin)
7) In other satin, these points make parallelogram.
8) Expressing [n-harness and a-counts satin as a/n, Fibonacci series, composed of regular satin may be obtained is:
In this series, the satin at even order is of squre type satin, and the both counts of satins at odd order are same, a=b.
