A wax comb and its hexagonal cells.

Optimize, optimize! That seems to be the bees' motto when they build their honeycombs. Let's take a closer look at their thrifty "methods." Geometry will prove invaluable in calculating the areas and angles of the cells.


Articles recommended for you.

Bees do not shape their honeycomb cells into hexagons deliberately, but because of the viscoelasticity of wax: the cells, initially circular, compress against one another, the wax melts and angles begin to form; the circular shape becomes hexagonal.

Even when some "natural" problems prove impossible to solve, mathematicians have found ways around them, producing approximations of varying accuracy. To do so, they have sometimes had to draw on a host of geometric tricks and devise ingenious mechanisms.

While the formula for the area of an arbitrary triangle has been known for a long time, that of an arbitrary quadrilateral took longer to emerge. Yet the two formulas share a kinship — visual, if nothing else — that is quite fascinating.

For a given perimeter, the disk is the figure with the greatest area. This result, popularized by a trick attributed to Dido, the founder and first queen of Carthage, is the "isoperimetric theorem." It gave rise to many more general inequalities.
Discussion
Sign in to post a comment and talk with other readers.
No comments yet. Be the first to respond.