on twill plaited mats and baskets Paulus Gerdes Mozambican Ethnomathematics
Research Centre, C.P. 915,
Twill plaited toothed squares may be chained to each other to form linear strings. Figure 1a shows the twill plaited toothed square (3,2,3). Successive copies of this toothed square may be embraced by loop of plaiting width 3 and be chained (see Figure 1b). In this example, we have a vertical connection established by a vertical strand passing over five horizontal strands. Let us say that this constitutes the 1×5 connection. Sometimes single strings are plaited. Figure 2 displays a single string that appears on a Mbole mat from Northeast Congo (Zaire): The toothed squares (5,3,5) are embraced by a loop of plaiting width 5 and chained by a 9×1 connection. It is a short string: Only two units are chained. Figure 3 presents another Mbole motif. This time three (9,2,4) toothed squares are chained by a loop of width 5 and a 1×7 connection.
Two-colour images At other occasions a longer string is combined with its ‘negative’ to form a double string, as Figure 4a illustrates for the string of Figure 1b. By continuing to plait congruent strings, a plane pattern is produced (see Figure 5). This plaiting structure appears on a Cherokee basket (cf. Hill, p.173). Table 1 presents the
list of similar double string patterns I found so far. Figures
6 to 9 present examples. The visual image of each
of these patterns is that of a two-colour pattern belonging to the symmetry
class pc’mm.
Strings separated by zigzags Figure 4b presents two copies of the initial single string of Figure 1b separated by a zigzag with a plaiting width of 3 strands. Table 2 presents the list of patterns constituted of strings separated by one or more zigzags I encountered so far. If the number of zigzags is even, ‘positive’ and ‘negative’ copies of the string alternate (see the example in Figure 10). If the number of zigzags is odd, only ‘positive’ copies of the strings appear. Figures 11 and 12 present two examples of patterns from the Bora living in the Peruvian Amazon. In fact they present only the structure of the plaiting of the circular trays in our collection. Their visual image is rather different (See Figures 13 and 14 respectively), as natural black and whitened strands alternate in both weaving directions.
Museums RMCA: Royal Museum for Central Africa, Tervuren, Belgium References Gettys, Marshall (Ed.), Basketry of Southeastern Indians, Museum of the Red River, Idabel, Oklahoma, 1984 Grottanelli, Vinigi [Ed.] (1965), Ethnologica - L’Uomo e la Civilta, Edizioni Labor, Milano Hill, Sarah H., Weaving New Worlds: Southeastern Cherokee Women and their Basketry, The University of North Carolina Press, Chapel Hill, 1997 Jahn, Jens (Ed.), LOSA, Flechtwerke der Mbole, Verlag Fred Jahn, München, 1988 Taylor, Colin (Ed.), Native American
Arts and Crafts, Salamander Books, London, 1995
(a)
(b) Figure 2
(Drawn after a detail of a photograph in Jahn, p. 48)
(a) ‘Positive’ and ‘negative’
Plaiting texture and visual image of a Cherokee design
Pattern (1,2,4, 7x1) x2
Pattern (1,5,4, 7x1) x2
Pattern (3,1,0, 3x3) x2
Pattern (3,2,4, 7x1) x2
Visual image of the Bora pattern in Figure 11
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