*Regular hexagons provide the least-perimeter way to divide the plane into unit areas.*

The recent reports on the disappearance of bee populations have omitted mention of their role in the longest-standing open problem in mathematics, dating from the first millennium B.C.E. and solved in the nick of time (actually with a year to spare; see *Scientific American*) for the second millennium in 1999. The ancient conjecture, now a theorem, says that the hexagonal honeycomb of Figure 1 provides the most efficient (least-perimeter) way to divide the plane into unit areas. A proof was announced by Thomas Halesin 1999, the same Hales who the year before had proved the 1611 Kepler sphere-packing conjecture, a mere 387 years old. This in turn was on the heels of the celebrated 1995 proof by Princeton mathematicianAndrew Wiles of Fermat’s 1637 “Last Theorem,” similarly a mere 358 years old.

Figure 1. Regular hexagons provide the least-perimeter way to divide the plane into unit areas. Image from wikipedia.org.

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Tags: edublog, geometry, math, math and nature, mathematics

This entry was posted on March 8, 2012 at 1:39 am and is filed under General interest, Geometry, Life Science, Math meets art. You can follow any responses to this entry through the RSS 2.0 feed.
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