Ad Quadratum Ad Infinitum

Eliana Manuel Pinho
Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture (2010)
Pages 459–462 Short Papers


We consider planar patterns with two colours, white and black, that are periodic along two non-colinear directions and such that the white and black regions are related by one Euclidean isometry. The fundamental cells of these patterns have half the area in white and the other half in black. In Roman mosaics with two colours exhibiting square- based repetitive patterns, the balance between the two colours is often solved via the ad quadratum geometrical construction. Several patterns observed in Roman mosaics with two colours, mainly from Conimbriga, are presented to illustrate this idea.