The upper estimate and conjecture on Hausdorff measure of Sierpinski gasket

被引:0
|
作者
Wang, XH [1 ]
机构
[1] Hangzhou Univ, Dept Math & Informat Sci, Hangzhou 310028, Peoples R China
关键词
Sierpinski gasket; Hausdorff measure; symmetry; curved nonagon; binary decimal;
D O I
暂无
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
For a binary decimal x with n bits, the pre-fractal of the level n + 1 of Sierpinski gasket S can be partially covered by a curved nonagon with the diameter 1 - x/2. The number of the small triangles which are not completely covered can be counted and a simple expression of the upper estimate function upsilon(n)(x) for Hausdorff measure of S can be derived. By minimized searching, a sequence with optimized estimates is obtained. The values and expressions of the first 16 terms are given, especially, the 16th term is exp(ln 97793(.)ln 3/ln 2)/99250914 = 0.817 930 0(...). On the above basis, a conjecture on the exact value of Hausdorff measure is proposed.
引用
收藏
页码:812 / 819
页数:8
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