A spectral triple associated to a C*-algebra may, for a given C*-algebra, be obtained in different ways. Is there a “right” smooth structure associated to a given C*-algebra? In collaboration with Cristina Ivan, Michel Lapidus, and Elmar Schrohe, we have studied ways of assigning spectral triples to commutative C*-algebras where the spectrum is a fractal set in the plane. A fractal has no smooth structure, but some parts of a differentiable structure can be expressed in terms of a spectral triple, and in this way make sense, also for a fractal set. For the Sierpinski Gasket we have constructed an infinite family of spectral triples to choose from, and I will try to indicate which one to choose if you want to emphasize that the spectral triple shall reflect a specific geometric property of the gasket.