Strings of connected toothed squares
on twill plaited mats and baskets

Paulus Gerdes

Mozambican Ethnomathematics Research Centre, C.P. 915,
Maputo, Mozambique
pgerdes@virconn.com

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.

Table 1

 Toothed square Loop plaiting width Connection Country People [Region] Source (1,1,0) 2 1×3 Congo Yombe RMCA 80.12.24 (1,2,4) 4 1×7 Indonesia [Flores] Dawson 165 (1,5,4) 4 1×7 Peru Bora pg June 1, 2000 (3,1,0) 3 3×3 USA Cherokee Hill 308 (3,2,3) 3 1×5 USA Cherokee Hill 173 (3,2,4) 4 1×7 USA Choctaw Gettys 39

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 pcmm.

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.

Table 2

 Toothed square Loop plaiting width Connection Number of zigzags Zigzag width Country People [Region] Source (1,1,0) 2 1×3 0 - Congo Yombe RMCA 80.12.24 (1,2,4) 4 1×7 0 - Indonesia [Flores] Dawson 165 (1,5,4) 4 1×7 0 - Peru Bora pg June 1, 2000 (3,1,0) 3 3×3 0 - USA Cherokee Hill 308 (3,2,3) 3 1×5 0 - USA Cherokee Hill 173 (3,2,4) 4 1×7 0 - USA Choctaw Gettys 39 (1,2,2) 2 1×3 1 2 Peru Bora pg June 5, 2000 (1,2,2) 3 1×5 1 3 USA Chitimacha Taylor 12 (1,2,3) 3 1×5 1 3 Peru Bora pg June 5, 2000 (7,3,5) 5 1×9 1 5 Peru Bora pg June 1, 2000 (11,1,0) 3 1×5 1 3 Congo Yombe RMCA 80.12.38 (1,1,0) 3 1×5 2 3 Brazil Apinajé Grottanelli 8: 66 (1,5,4) 4 1×7 3 4 Peru Bora pg June 1, 2000 (5,3,2) 2 3×1 13 2 Peru Bora pg June 5, 2000

Museums

pg: Author’s collection

RMCA: Royal Museum for Central Africa, Tervuren, Belgium

References

Dawson, Barry & Gillow, John, The traditional architecture of Indonesia, Thames and Hudson, 1994

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 1

(Drawn after a detail of a photograph in Jahn, p. 47)
Figure 2

(Drawn after a detail of a photograph in Jahn, p. 48)
Figure 3

(a) ‘Positive’ and ‘negative’

(b) Two ‘positives’ separated by a zigzag
Figure 4

Plaiting texture and visual image of a Cherokee design
Figure 5

Pattern (1,2,4, 7x1) x2
Figure 6

Pattern (1,5,4, 7x1) x2
Figure 7

Pattern (3,1,0, 3x3) x2
Figure 8

Pattern (3,2,4, 7x1) x2
Figure 9

Apinajé pattern
Figure 10

Bora pattern
Figure 11

Bora pattern
Figure 12

Visual image of the Bora pattern in Figure 11
Figure 13

Visual image of the Bora pattern in Figure 12
Figure 14

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