# Sierpinski, Waclaw Franciszek (1882–1969)

Waclaw Sierpinski was a Polish mathematician who made outstanding contributions to set theory, which included research on the axiom of choice and the continuum hypothesis, number theory, and topology. Two well-known fractals, the Sierpinski Carpet (see below) and the Sierpinski Gasket, are named after him.

## Sierpinski Carpet

The Sierpinski Carpet is a fractal, named after Waclaw Sierpinski, that is derived from a square by cutting it into nine equal squares with a 3 × 3 grid, removing the central piece, and then applying the same procedure ad infinitum to the remaining eight squares. It is one of two generalizations of the Cantor set to two dimensions; the other is the Cantor Dust. The Carpet's Hausdorff dimension is log 8/log 3 = 1.8928...