# Schläfli, Ludwig (1814–1895)

Ludwig Schläfli was a German mathematician whose worked centered on geometry, arithmetic, and the theory of functions. He made an important contribution to non-Euclidean geometry when he proposed that spherical three-dimensional space could be thought of as the surface of a hypersphere in Euclidean four-dimensional space.

Schläfli started out as a schoolteacher and amateur mathematician. He was
also was an expert linguist and spoke many languages, including Sanskrit.
In 1843 he served as a translator for the great mathematicians Jakob Steiner,
Karl Jacobi, and Peter Dirichlet during their visit to Rome and learned a great deal from them. Ten years
later he became professor of mathematics at Bern. However, his true importance
was only appreciated following the publication of his magnum opus *Theory
of Continuous Manifolds* in 1901, several years after his death.

## SchlĂ¤fli symbol

The Schläfli symbol is a notation, devised by Ludwig Schläfli,
which describes the number of edges of each polygon meeting at a vertex of a regular or semi-regular tiling or solid. For a Platonic
solid, it is written {*p*, *q*}, where *p* is the number
of sides each face has, and *q* is the number of faces that touch at
each vertex.