2013, Volume 8, Issue 4
Frontiers of Mechanical Engineering >> 2013, Volume 8, Issue 4 doi: 10.1007/s11465-013-0273-7
A new proof of Honeycomb Conjecture by fractal geometry methods
1. Research Center for Solid Mechanics, Beihang University, Beijing 100191, China; School of Engineering, Brown University, Providence, RI 02912, USA
2. School of Instrument Science and Optical Engineering, Beihang University, Beijing 100191, China
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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.
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