Buffon needle lands in ε-neighborhood of a 1-Dimensional Sierpinski Gasket with probability at most |ε|⁻ᶜ

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In recent years, relatively sharp quantitative results in the spirit of the Besicovitch projection theorem have been obtained for self-similar sets by studying the Lᵖ norms of the "projection multiplicity" functions, fθ, where fθ(x) is the number of connected components of the partial fractal set that orthogonally project in the θ direction to cover x. In NPV, it was shown that n-th partial 4-corner Cantor set with self-similar scaling factor 1/4 decays in Favard length at least as fast as C/nᵖ, for p<1/6. In BV, this same estimate was proved for the 1-dimensional Sierpinski gasket for some p>0. A few observations were needed to adapt the approach of NPV to the gasket: we sketch them here. We also formulate a result about all self-similar sets of dimension 1.