Mozambican Ethnomathematics
Research Centre, C.P. 915,
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
Were regular square plane patterns on twill plaited mats
characterised by a set of four numbers (
represents the distance between horizontally neighbour sets of concentric
toothed squares and s 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, 3t×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 (
Basket container from Tibet with the semi-regular (1,3,2,
3x1) pattern
Small circular mat from Kenya with the semi-regular (1,3,4,
1x7) pattern
Example
of a regular pattern
Figure 1:
EMN: Ethnographic Museum, Nampula, Mozambique MNEP: Museu Nacional de Etnologia, Lisboa, Portugal RMCA: Royal Museum for Central Africa, Tervuren, Belgium
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