Liberal Arts Blog — Geometry IV: A Paean to the Hexagon
Liberal Arts Blog — Monday is the Joy of Math, Statistics, and Numbers Day
Today’s Topic — Geometry IV: A Paean to the Hexagon
Hexagons are ubiquitous. Honeycombs are hexagonal. Carbon molecules are too. Nuts and bolts. Tile floors are often hexagonal. Snowflakes. The basalt columns at the Giant’s Causeway in Ireland. You can find them on the backs of turtles and on soccer balls. Even France is hexagonal (or so French children are taught in school). The cell phone network? Hexagonal. Liver cells (hepatocytes)? Hexagonal. I’ll stop there. Experts — please chime in. Correct, elaborate, elucidate.
HONEY BEES, PACKING EFFICIENCY, MINIMIZING WAX, MINIMIZING ENERGY
1.” If you want to pack together cells that are identical in shape and size so that they fill all of a flat plane, only three regular shapes (with all sides and angles identical) will work: equilateral triangles, squares, and hexagons.”
2. “Of these, hexagonal cells require the least total length of wall, compared with triangles or squares of the same area.”
3. “So it makes sense that bees would choose hexagons, since making wax costs them energy, and they will want to use up as little as possible — just as builders might want to save on the cost of bricks.”
NB: “This was understood in the 18th century, and Darwin declared that the hexagonal honeycomb is “absolutely perfect in economizing labor and wax.”
SIX SIDES, SIX ANGLES OF 120 DEGREES EACH
1. “With this structure, the pull of surface tension in each direction is most mechanically stable.”
2. “which is why even though bees make their honeycombs with circular units, the end result when the wax hardens into place is hexagonal.”
3. Liver cells (hepatocytes) are roughly hexagonal.
CELLULAR PHONE NETWORKS: EQUAL SIGNAL STRENGTH PLUS NO BLACK SPOTS
1. If the cells were circular, there would be areas of no coverage (black spots).
2. If the cells were square, the distance from the center to the corner would be greater than the distance to the sides.
3. As a result, signal strength would not be equal at every point.
Is France really a hexagon?
Any thoughts on hexagons? Please share the coolest thing you learned this week related to math, statistics, or numbers in general.
Or, even better, the coolest or most important thing you learned in your life related to math.
This is your chance to make someone else’s day. And to consolidate in your memory something you might otherwise forget. Or to think more deeply than otherwise about something dear to your heart. Continuity is key to depth of thought.