Graphs on the Ceilings of Gothic Churches in Slovenia

Tomaz Pisanski

Univerza v Ljubljani, Slovenia

November 7,
4:15pm
refreshments at 3:45pm
2-338

ABSTRACT 

Ceilings of Gothic churches containing ribbed vaults present interesting mathematical patterns. A ribbed vault is a framework of diagonal arched ribs carrying the cells which cover ceiling in the spaces between them. Such a structure can be represented as a graph on a surface or as a tiling of a plane. The bosses and columns are vertices, the ribbed arches are edges and the cells are faces of the embedded graph. Although such geometric patterns can be found in Gothic churches throughout Europe we present some special masterpieces of star vault networks from the ceilings of late Gothic churches in Slovenia. In some cases the complicated structure of such patterns can be explained by applying some transformations that turn simple small graphs into larger, more complicated ones. In most cases it is sufficient to use the transformations that can produce from the graph of tetrahedron successively the graphs of all other four Platonic and the thirteen Archimedean solids. By combining simple transformations into more complicated ones an interesting tool for investigating maps on surfaces, tilings and polyhedra is obtained. For instance, one of the composed transformations is known in theoretical chemistry under the name of leapfrog transformation.


Speaker's Contact Info: Tomaz.Pisankski(at-sign)fmf.uni-li.si


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