Mathematics and Archaeology

Reconstruction of the original aspect of ancient floors is a classical problem for archaeologists and restoration architects. Via the mathematical theory of periodic tessellations we reconstruct the original aspect of floors compatible with the fragments on site at theTrajan Markets, Rome. Our solution is unique under standard assumptions on regularity of the patterns. The experts had previously considered the fragments of insufficient information. The result applies the twentieth century mathematical thought "symmetry=less information". This theorem has been largely used in visual analysis and classification; here is a first instance of its use for reconstruction, i.e. for its predictive power.