Analysing symmetric, mat weaving designs made by Makwe women in the Northeast of Mozambique: The example of the chicken's eye pattern

Paulus Gerdes

Visual Mathematics, Tome 15 (2013) no. 1.

Résumé

Makwe speaking women in the Palma District in the Cabo Delgado Province in the Northeast of Mozambique have been producing, for centuries, mats by sewing together bright monochrome and decorated two-colour strips. Earlier the author analysed symmetry classes and colour inversion of decorated strips where natural and dark coloured strands alternate. The present paper analyses a different kind of decorated strip. A particularly woven band displays on both faces the same strip pattern albeit with its orientation inverted. The pattern is called the chicken's eye and has a horizontal axis of symmetry. The paper explains that the inversion of the orientation of the pattern results from the particular weaving texture and that the symmetry of design is a consequence of the chosen colouring code in association with the selected weaving texture. To analyse the woven band, the author constructs underlying number friezes that present interesting symmetry and anti-symmetry properties. The inventor(s) of the chicken's eye pattern constructed consciously and carefully the weaving texture. This texture did not result from mere experimentation, but some type of calculation and of geometric-symmetry considerations was involved in one way or another. The author illustrates how changing the colour code, the weaving texture or the dimensions produces other patterns with the same properties as the chicken's eye pattern. The paper invites to further mathematical study of particular number friezes and their generalization.

Détail

Classification : 20H15