| Plaited strip patterns on Tonga handbags
in Inhambane (Mozambique) – Update 2004 Paulus Gerdes Mozambican
Ethnomathematics
The following chapter presents an update on strip patterns found on twill-plaited handbags and baskets made by Tonga artisans, mostly women. It includes a catalogue of 74 new strip patterns that appear on sipatsi collected between January 2003 and August, 2004. All seven symmetry classes are represented. Introduction Two other chapters "Exploring plaited plane patterns among the Tonga in Inhambane (Mozambique)" and "Colour transformation of strip patterns in Tonga basketry (Mozambique)" already deal with Tonga handbags called gipatsi (Plural: sipatsi), produced mostly by women from the Mozambican province of Inhambane. The books (Gerdes & Bulafo, 1994) and (Gerdes, 2003a) analyse sipatsi. To produce these handbags the artisans use mostly as basic weave the ‘over two, under two’ twill (notation: 2/2). By introducing some systematic changes in the weave along bands of the texture, they create attractive strip patterns. In one weaving direction all the strands are coloured, while in the opposite direction all strands maintain their natural colour (white-yellow). The Tonga weavers are very creative in inventing new strip patterns. Whereas the catalogue in (Gerdes & Bulafo, 1994) included 96 different strip patterns (collected in the period 1977-1993), the catalogue in (Gerdes, 2003a) includes 362 different strip patterns collected until July 2002. The update (Gerdes, 2003b) presented 58 new strip patterns that appear on sipatsi collected between August and December 2002. The following 2004-update presents a further 74 new strip patterns that appear on sipatsi collected between January 2003 and August 2004, bringing the total of gipatsi strip patterns observed to 494. Representation of strip patterns Figure 1 illustrates part of a gipatsi. In the illustration, the darker strands, in fact, are purple, dark green, or, dark blue (see the photographs). The use of different colours makes sipatsi more attractive. For the weavers of sipatsi, the beauty of the ornaments resides principally in the quality of the contrast generated by the plaiting of sets of strands of natural colour ("white-yellow" strands) with coloured strands. For this reason, we may represent all coloured strands with the same colour. As the direction of individual strands is (almost) not visible, we may remove them from the illustration. In this way, the decorated strip, of which Figure 2 shows only a portion, is transformed into the strip of Figure 3. For any gipatsi, on the left and right of the motif of an ornamental strip, there is always another exemplar of the same motif. In this sense, one may consider an ornamental strip on a gipatsi as infinite. Consequently, one may consider the part of the strip illustrated on a piece of (planar) paper as representing the whole strip that extends infinitely to the left and to the right, always repeating at fixed distance the same decorative motif. A strip of this nature is called a one-dimensional strip pattern. Strip patterns that derive from ornamental strips on sipatsi we will call gipatsi-patterns. We may say that the toothed parallelogram in Figure 4 generates the gipatsi-pattern in Figure 3. In our example, the toothed parallelogram has the dimensions 4 by 7, that is, 4 contiguous oblique strands, each composed of 7 unit squares (see Figure 5). The sides of the unit square are equal to the width of the strand. We will call the first dimension the period of the decorative motif and the second dimension its diagonal height. In the given example, we have 4 as the period. In other words, the period indicates how many coloured strands are necessary to generate the decorative motif. For each pattern in the complementary catalogue of gipatsi-patterns we will indicate a generating toothed parallelogram. The gipatsi-patterns will appear in increasing order of their period. Patterns of the same period come in increasing order of their diagonal heights. A gipatsi-pattern will be represented by p × h [n], being p its period, h its diagonal height and n its order among the gipatsi-patterns with dimensions p × h. For instance, the pattern with the code 2×9 [4] refers to the fourth pattern with dimensions 2 by 9. Figure 6 presents the 74 new gipatsi-patterns. Symmetries Among the 74 new gipatsi-patterns, all seven (one-colour) one-dimensional symmetry classes are represented. For an introduction to these symmetry classes and explanation of the international notation, see e.g. Washburn & Crowe, 1988. Table 1 gives the distribution of the additional gipatsi-patterns by symmetry classes. Forty-two of the new gipatsi strip patterns (classes 1, 2, 3 in Table 1) have vertical symmetry axes (57 %), thirty (classes 1, 4) have a horizontal symmetry axis (41 %), and thirty-four (classes 1, 2, 5) have a two-fold rotational symmetry (46 %). Thirty of the new gipatsi strip patterns are single (41%; for an introduction to the concept of single, see Gerdes, 2003b). The photographs 1 to 10
present examples of sipatsi and of handbags with gipatsi
patterns collected in the period from January 2003 to August 2004. Along
with the new gipatsi patterns represented in Figure
6, also earlier patterns continue to be used as their respective numbers
indicate.
References Gerdes, Paulus (2003b), Plaited strip patterns on Tonga handbags in Inhambane (Mozambique) – An update, Visual Mathematics, March 2003, 5(1) Gerdes, Paulus and Bulafo, Gildo (1994), Sipatsi: Technology, Art and Geometry in Inhambane, Maputo: Universidade Pedagógica Washburn, Dorothy K. and Crowe, Donald
W. (1988), Symmetries of Culture. Theory and Practice of Plane Pattern
Analysis, Seattle: University of Washington Press
Table 1
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6: Catalogue of new gipatsi-patterns
Photograph 1: Gipatsi with pattern
no. 117 (top)
Photograph 2: Gipatsi
Photograph 3: Detail of the gipatsi
in Photograph 2. Top pattern is no. 438.
Photograph 4: Gipatsi
Photograph 5: Detail of the gipatsi
in Photograph 4. Top pattern is no. 335.
Photograph 6: Gipatsi with pattern no. 79.
Photograph 7: Handbag with gipatsi
patterns (No. 434 is the pattern in the middle)
Photograph 8: Handbag with gipatsi
patterns nos. 192 and 258.
Photograph 9: Handbag with gipatsi
pattern no. 289.
Photograph 10: Handbag with gipatsi patterns nos. 260 and 178.
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