The Koch snowflake curve is tube-null
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- by Viktor Harangi PDF
- Proc. Amer. Math. Soc. 139 (2011), 1375-1381 Request permission
Abstract:
We show that the Koch curve is tube-null; that is, it can be covered by strips of arbitrarily small total width. In fact, we prove the following stronger result: the Koch curve can be decomposed into three sets such that each can be projected to a line in such a way that the image has Hausdorff dimension less than $1$. The proof contains geometric, combinatorial, algebraic and probabilistic arguments.References
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Additional Information
- Viktor Harangi
- Affiliation: Department of Analysis, Eötvös Loránd University, Pázmány Péter sétány 1/c, H-1117 Budapest, Hungary
- Email: bizkit@cs.elte.hu
- Received by editor(s): April 15, 2010
- Published electronically: December 1, 2010
- Additional Notes: The author was supported by OTKA grant 72655.
- Communicated by: Tatiana Toro
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 1375-1381
- MSC (2010): Primary 28A12, 28A80
- DOI: https://doi.org/10.1090/S0002-9939-2010-10712-8
- MathSciNet review: 2748429