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One of the key ingredients of A. Connes' noncommutative geometry is ageneralized Dirac operator which induces a metric(Connes' distance) on thestate space. We generalize such a Dirac operator devised by A. Dimakis et al,whose Connes' distance recovers the linear distance on a 1D lattice, into 2Dlattice. This Dirac operator being "naturally" defined has the so-called "localeigenvalue property" and induces Euclidean distance on this 2D lattice. Thiskind of Dirac operator can be generalized into any higher dimensional lattices.Comment: Latex 11pages, no figure

Pythagoras's theorem on a two-dimensional lattice from a `natural' Dirac operator and Connes's distance formula