Semi-regular square
plane patterns
on twill plaited
mats and baskets
Paulus Gerdes
Mozambican Ethnomathematics
Research Centre, C.P. 915,
Maputo, Mozambique
pgerdes@virconn.com
Abstract
The paper defines and analyses a class and several subclasses of semi-regular patterns appearing on twill plaited mats and baskets. The patterns are composed of sets of congruent concentric toothed squares that are at different distances in both weaving directions. A comparative overview and examples of their regional distribution are given.
In this paper I introduce the concept of semi-regular square plane patterns on twill plaited mats and baskets and present examples from several cultures around the world. Photographs 1 and 2 present two baskets with semi-regular square plane patterns. Many examples come from Bora mat weaver living in the Peruvian Amazon, who seem to have been particularly keen in inventing and using semi-regular square plane patterns. The semi-regular square plane patterns differ from the regular ones in one fundamental aspect. Whereas in the case of the regular ones, the distance between the horizontally neighbour sets of concentric toothed squares is always the same as the distance between the vertically neighbour sets of concentric toothed squares, in the case of the semi-regular square plane patterns this horizontal distance is different from the vertical distance. Figure 1 presents an example of a regular pattern: Both distances are equal to 3. Figure 2 presents an example of a semi-regular pattern: The horizontal distance is 3, whereas the vertical distance is 1.
By consequence, semi-regular square plane patterns have only two axes of symmetry. Their two-colour images belong to symmetry class cmm.
Were regular square plane patterns on twill plaited mats characterised by a set of four numbers (p,q,r,s), semi-regular square plane patterns may be characterised analogously by (p,q,r,s×t), where s represents the distance between horizontally neighbour sets of concentric toothed squares and t the distance between vertically neigbour sets of concentric toothed squares. In this sense the regular and semi-regular square plane patterns in the example above may be characterised by (1,2,3,3) and (1,2,3, 3×1), respectively. There is no difference between (p,q,r, s×t) and (p,q,r, t×s), as they correspond to the view of opposite sides of the mat rotated about a right angle.
In the following I present the classes of semi-regular
square plane patterns so far encountered by me on twill plaited mats and
baskets from several cultures around the world. The list is by class (p,q,r,s×t),
by country, by people (linguistic or ethnic population group) [or region],
the source of the book or paper, or of the museum in which I saw (a photograph
of) a mat or a basket with the semi-regular square plane pattern. In the
case of a mat or basket belonging to my personal collection I indicate
as source pg, followed by the place and date that I acquired the object.
In the case that only (a few) congruent sets of concentric toothed squares
are woven as a strip pattern, I indicate ‘strip’, supposing that in the
same culture the plane pattern may be known too (or imaginable in the head
of the mat weaver). In the cases found so far, p, s and t
are always odd numbers.
| Class | Country | People | Source |
| (1,2,1, 3×1) | Congo / Zaire | Kongo | Sentence 111 |
| (1,2,2, 3×1) | Congo / Zaire | Yombe | RMCA 80.12.30 (see Figure 3) |
| Peru | Bora | pg Iquitos (Peru) Jun 2000 | |
| (1,2,2, 5×3) | Congo / Zaire | Mbole | Mantuba-Ngoma 21 (see Figure 4) |
| (1,2,3, 5×1) | Peru | Bora | pg Iquitos (Peru) Jun 2000 (see Figure 5) |
| Mozambique | Changana | pg Palmeira (Mozambique) 2003 | |
| (1,2,4, 7×1) | Indonesia | [Flores] | Dawson 164 |
| (1,3,2, 3×1) | Indonesia | LaPlantz 88, Gerdes [1] 266 | |
| Tibet | pg Bergen (Norway) Sep 1985, Gerdes [1] 261 (see Photograph 1) | ||
| (1,3,3, 3×1) | Brazil | Baniwa | MNEP |
| (1,3,3, 5×1) | Peru | Bora | pg Iquitos (Peru) Jun 2000 |
| (1,3,4, 7×1) | Congo | Kongo | Sentance 111 |
| Kenya | pg Nairobi (Kenya) Aug 1985, Gerdes [1] 141 (see Photograph 2) | ||
| USA | Choctaw | Gettys 39 | |
| (1,3,5, 9×1) | Congo / Zaire | Mbole | Mantuba-Ngoma 47 |
| (1,4,2, 3×1) | China ? | pg Athens (USA) Sep 1997, Gerdes [1] 263 | |
| (1,4,4, 7×1) | Peru | Bora | pg Iquitos (Peru) Jun 2000 |
| (1,5,3, 5×1) | Peru | Bora | pg Iquitos (Peru) Jun 2000 |
| (1,5,4, 7x1) | Peru | Bora | pg Iquitos (Peru) Jun 2000 |
| (1,6,4, 7×1) | Peru | Bora | pg Iquitos (Peru) Jun 2000 |
| (1,8,2, 3×1) | Indonesia | Rooyen 48 | |
| Guiné Bissau | Rodrigues Martins Photo 66 | ||
| (1,10,2, 3×1) | Madagascar | pg Paris 1994 | |
| (3,2,2, 3×1) | India | [Northeast India] | Sentance 115 |
| (3,2,3, 3×1) | USA | Choctaw | Gettys 35 |
| (3,2,3, 5×1) | Gabon | Obamba | Perrois 44 |
| Peru | Bora | pg Iquitos (Peru) Jun 2000 | |
| USA | Cherokee | Duggan 17, Hill 245 | |
| Venezuela | Yekuana | Wilbert 148 | |
| (3,2,4, 7×1) | USA | Choctaw | Gettys 35 |
| (3,3,2, 3×1) | Brazil | Kayapó -Xikrin | Braun 96 |
| (3,3,3, 3×1) | USA | Choctaw | Gettys 41 (see Figure 6) |
| Brazil | Baniwa | Ricardo 58, 59 | |
| (3,3,3, 5×1) | Peru | Bora | pg Iquitos (Peru) Jun 2000 |
| (3,4,2, 3×1) | Indonesia | [Lombok] | Rooyen 24, Hoop 19 (see Figure 7) |
| Mozambique | Makhuwa | EMN S3/1644, Gerdes [1] 125 | |
| Tswa | Gerdes [1] 97 | ||
| (3,4,3, 5×1) | Colombia | Desana | Reichel-Dolmatoff 60 |
| Peru | Bora | pg Iquitos (Peru) Jun 2000 | |
| (3,4,4, 3×1) | Peru | Bora | pg Iquitos (Peru) Jun 2000 |
| (3,4,5, 9×1) | Peru | Bora | pg Iquitos (Peru) Jun 2000 |
| (3,5,2, 5×1) | Mozambique | Changana | pg Palmeira (Mozambique) 2003 |
| (3,5,3, 5×1) | Colombia | Desana | Reichel-Dolmatoff 60 |
| USA | Cherokee | Hill 311 | |
| (3,5,4, 3×1) | Peru | Bora | pg Iquitos (Peru) Jun 2000 |
| (5,2,3, 1×5) | Mozambique | Changana | pg Palmeira (Mozambique) 2003 |
| (5,3,2, 3×1) | Peru | Bora | pg Iquitos (Peru) Jun 2000 |
| (5,3,4, 3×5) | Brazil | Wayó | MNEP 2001 |
| (5,4,5, 9×1) | Peru | Bora | pg Iquitos (Peru) Jun 2000 |
| (7,2,4, 7×1) | Peru | Bora | pg Iquitos (Peru) Jun 2000 |
| (7,3,4, 7×1) | Peru | Bora | pg Iquitos (Peru) Jun 2000 |
| (7,3,5, 9×1) | Peru | Bora | pg Iquitos (Peru) Jun 2000 |
| (7,4,3, 5×1) | Peru | Bora | pg Iquitos (Peru) Jun 2000 |
| (7,4,4, 3×1) | Peru | Bora | pg Iquitos (Peru) Jun 2000 |
| (7,4,4, 7×1) | Peru | Bora | pg Iquitos (Peru) Jun 2000 |
Basket container from Tibet with the semi-regular (1,3,2,
3x1) pattern
(Basket from the author’s collection)
Photograph 1
Small circular mat from Kenya with the semi-regular (1,3,4,
1x7) pattern
(Basket from the author’s collection)
Photograph 2
Figure 2: Example of a
semi-regular pattern
Figure 3: Pattern (1,2,2,
3x1)
Figure 4: Pattern (1,2,2,
5x3)
Figure 5: Pattern (1,2,3,
5x1)
Figure 6: Pattern (3,3,3,
3x1)
Museums
EMN: Ethnographic Museum, Nampula, Mozambique
MNEP: Museu Nacional de Etnologia, Lisboa, Portugal
RMCA: Royal Museum for Central Africa, Tervuren, Belgium
References
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