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Analysis in Theory and Applications

, Volume 20, Issue 2, pp 158–166 | Cite as

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

  • Ruan Huojun
  • Su Weiyi
Article

Abstract

In this paper, we firstly define a decreasing sequence {Pn(S)} by the 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)8≤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.

Key words

Hausdorff measure sierpinski gasket approximation method 

AMS(2000)subject classification

28A78 28A80 68W25 

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Copyright information

© Springer 2004

Authors and Affiliations

  1. 1.Department of MathematicsZhejiang UniversityHangzhouP. R. China
  2. 2.Department of MathematicsNanjing UniversityNanjingP.R. China

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