Skip to main content

A new proof of Honeycomb Conjecture by fractal geometry methods

Abstract

Based on fractal geometry, we put forward a concise and straightforward method to prove Honeycomb Conjecture—a classical mathematic problem. Hexagon wins the most efficient covering unit in the two-dimensional space, compared with the other two covering units—triangle and square. From this point of view, honeycomb is treated as a hierarchical fractal structure that fully fills the plane. Therefore, the total side length and area are easily calculated and from the results, the covering efficiency of each possible unit is provided quantitatively.

This is a preview of subscription content, access via your institution.

References

  1. Hales T C. (8 Jun 1999). The honeycomb conjecture. Discrete and Computational Geometry, 2001, 25: 1–22 arXiv:math/9906042

    MathSciNet  Article  MATH  Google Scholar 

  2. Hales T C. Cannonballs and Honeycombs. Notices of the American Mathematical Society, 2000, 47: 440–449

    MathSciNet  MATH  Google Scholar 

  3. Fejes Tóth L. What the bees know and what they do not know. Bulletin of the American Mathematical Society, 1964, 70(4): 468–481

    MathSciNet  Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tong Zhang.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Zhang, T., Ding, K. A new proof of Honeycomb Conjecture by fractal geometry methods. Front. Mech. Eng. 8, 367–370 (2013). https://doi.org/10.1007/s11465-013-0273-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11465-013-0273-7

Keywords

  • Honeycomb Conjecture
  • fractal geometry
  • hierarchical fractal structure