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
Photograph 1

Small circular mat from Kenya with the semi-regular (1,3,4, 1x7) pattern
Photograph 2

Figure 1: Example of a regular pattern

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)

Figure 7: Pattern (3,4,2, 3x1)

Museums

EMN: Ethnographic Museum, Nampula, Mozambique

MNEP: Museu Nacional de Etnologia, Lisboa, Portugal

RMCA: Royal Museum for Central Africa, Tervuren, Belgium

pg: Author’s collection

References

Braun, Barbara (Ed.), Arts of the Amazon, Thames and Hudson, London, 1995

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

Duggan, Betty J. & Riggs, Brett H., Studies in Cherokee Basketry with a Reprint of ‘Decorative Art and basketry of the Cherokee’ by Frank G. Speck, The Frank H. McClung Museum, The University of Tennessee, Knoxville, 1991

Gerdes, Paulus [1], Le cercle et le carré: Créativité géométrique, artistique, et symbolique de vannières et vanniers d’Afrique, d’Amérique, d’Asie et d’Océanie, L’Harmattan, Paris, 2000

Gettys, Marshall (Ed.), Basketry of Southeastern Indians, Museum of the Red River, Idabel, Oklahoma, 1984

Hill, Sarah H., Weaving New Worlds: Southeastern Cherokee Women and their Basketry, The University of North Carolina Press, Chapel Hill, 1997

Hoop, A. van der, Indonesische Siermotieven – Ragam-ragam Perhiasan Indonesia – Indonesian Ornamental Design, Koninklijk Bataviaasch Genootschap van Kunsten en Wetenschappen, 1949

LaPlantz, Shereen, Twill basketry: A handbook of designs, techniques, and styles, Lark Books, Asheville, 1993

Mantuba-Ngoma, Mabiala, Losa: Flechtwerke der Mbole, Verlag Fred Jahn, Muenchen, 1988

Perrois, Louis (Ed.), Gabon: Cultures et Techniques, ORSTOM, Libreville, 1969

Reichel-Dolmatoff, Gerardo, Basketry as metaphor: Arts and crafts of the Desana indians of the Northwest Amazon, University of California Musuem of Cultural History, Los Angeles, 1985

Ricardo, Beto (Ed.), Arte Baniwa. Cestaria de Arumã, Federação das Organizações Indígenas do Rio Negro, ISA, São Paulo, 2000

Rodrigues Martins. Maria do Rosário (Ed.), Cestaria tradicional em África, Catálogo, Instituto de Antropologia – Universidade de Coimbra, Coimbra, 1988

Rooyen, Pepin van (Ed.), Indonesian Ornamental Design, The Pepin Press, Amsterdam, 1998

Sentance, Bryan, Art of the basket, Traditional basketry from around the world, Thames & Hudson, London, 2000

Wilbert, Johannes, Survivors of Eldorado: Four Indian Cultures of South America, Praeger, New York, 1972

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