An approximation method to estimate the Hausdorff measure of the Sierpinski gasket

In this paper, we firstly define a decreasing sequence {Pn(S)} by the generation of the Sierpinski gasket where each pn(S) can be obtained in finite steps. Then we prove that the Hausdorff measure Hs(S)of the Sierpinski gasket S can be approximated by {Pn(S)} with Pn(S)/(1 1/2n-3)s ≤ Hs(S) ≤ pn(S).An algorithm is presented to get Pn(S) for n ≤ 5. As an application, we obtain the best lower bound of Hs(S) till now: Hs(S) ≥ 0.5631.