Sacred Numbers and Tessellations in Aquileia's XI Century Mosaics

Marcella Giulia Lorenzi and Mauro Francaviglia
Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture (2012)
Pages 251–258


Many religious and/or esoteric traditions attribute specific meanings to small integers. In particular, in Christianity, the number 7 symbolizes the Holy Spirit, the number 8 the union of the human body with the spiritual world, and the number 33 is Christ's (alleged) age at crucifixion. A mosaic pattern found on the floor of a XI century cathedral in northern Italy closely covers the interior of a regular octagon with a rotationally symmetric, 7x7 checkerboard array of squares. When one considers the largest possible set of sub-squares inside that figure's 8 sides that forms a cross-like shape, the number 33 coincidentally manifests itself. We argue that the ancient mosaic designers chose the 7x7 subdivision because they recognized this hidden count of 33, rather than because no other low-resolution subdivision, with the possible exception of the 10x10, would have worked as well mathematically (without, however, generating directly the numbers 8 and 33).