3 ms·

You don't really need much math to see why this is happening. First, the bonds in a benzene ring aren't discrete like we draw them, alternating between single

by jfarmer 13y ago

You don't really need much math to see why this is happening. First, the bonds in a benzene ring aren't discrete like we draw them, alternating between single bonds and double bonds. It's also important to realize that although we typically represent benzene in 2D all molecules really have a 3D geometry. Electron orbitals can overlap in different ways depending on the geometry of the atom and its electronics. See this for a picture: http://en.wikipedia.org/wiki/File:Benzene_Representations.svg http://en.wikipedia.org/wiki/File:Benzene_Representations.sv... So, the electrons in a benzene ring really form more of a cloud around the entire ring. You'd expect this to pull the atoms into a perfect circle with the carbon atoms all being equidistance from each other, all else being equal. However, each carbon atom also has a hydrogen atom attached to it. So now you have a sort of a circle with 6 "strings" attached at points equidistant around the circle all pulling outward, perpendicular to the circle. Imagine a perfectly circular piece of string with 6 strings attached equidistantly around the circle. You apply an equal force perpendicular to the surface of the circle. Hopefully you can see how this would result in the original circular string being "deformed" into a hexagon. It's a far leap from there to say why hexagons are "so common in nature." Are they? Relative to what? I don't know that any of this has anything to do with the shape of that storm you linked to.

bsg75 13y ago
> It's a far leap from there to say why hexagons are "so common in nature." I was thinking of things (compared to other geometric shapes) like the storm, honey bee cells (honeycombs), basalt columns [1], turtle shells (although irregular), and a common snowflake shape. [1] http://en.wikipedia.org/wiki/Giants_Causeway http://en.wikipedia.org/wiki/Giants_Causeway
- jfarmer 13y ago
  There are three regular polygons you can use to tile a plane: triangles, squares, and hexagons. The regular hexagonal packing is the densest sphere packing in the plane, so any time you have objects constrained to a plane which for the sake of maximizing or minimizing some force want to be equidistant from each other you'll get something close to a hexagon.
  - jfarmer 13y ago
    I'll add that sometimes a shape like that might result from a more evolutionary process. In a 2D plane a circle is the structure which most equally distributes force, so it's the shape most able to hold up under pressure. But a tile of circles isn't so fortunate. Of all the possible tilings, the hexagonal tiling holds up the best precisely because it's the densest sphere packing in the plane. Other arrangements might appear, but over the course of time you're more likely to see hexagonal tilings since those are the ones that best survive external forces.
- mtdewcmu 13y ago
  Snowflakes come out hexagonal because of the way water crystallizes: http://en.wikipedia.org/wiki/File:Hex_ice.GIF http://en.wikipedia.org/wiki/File:Hex_ice.GIF It has to do with the bond angles in water molecules. The bond angles are, in turn, determined by quantum mechanical wave functions. These quantum mechanical wave functions apply to all of chemistry, including benzene rings. So the shapes of snowflakes and the shapes of benzene rings are not totally independent events.

by jfarmer 13y ago

bsg75 13y ago

> It's a far leap from there to say why hexagons are "so common in nature." I was thinking of things (compared to other geometric shapes) like the storm, honey bee cells (honeycombs), basalt columns [1], turtle shells (although irregular), and a common snowflake shape. [1] http://en.wikipedia.org/wiki/Giants_Causeway http://en.wikipedia.org/wiki/Giants_Causeway

jfarmer 13y ago
There are three regular polygons you can use to tile a plane: triangles, squares, and hexagons. The regular hexagonal packing is the densest sphere packing in the plane, so any time you have objects constrained to a plane which for the sake of maximizing or minimizing some force want to be equidistant from each other you'll get something close to a hexagon.
- jfarmer 13y ago
  I'll add that sometimes a shape like that might result from a more evolutionary process. In a 2D plane a circle is the structure which most equally distributes force, so it's the shape most able to hold up under pressure. But a tile of circles isn't so fortunate. Of all the possible tilings, the hexagonal tiling holds up the best precisely because it's the densest sphere packing in the plane. Other arrangements might appear, but over the course of time you're more likely to see hexagonal tilings since those are the ones that best survive external forces.
mtdewcmu 13y ago
Snowflakes come out hexagonal because of the way water crystallizes: http://en.wikipedia.org/wiki/File:Hex_ice.GIF http://en.wikipedia.org/wiki/File:Hex_ice.GIF It has to do with the bond angles in water molecules. The bond angles are, in turn, determined by quantum mechanical wave functions. These quantum mechanical wave functions apply to all of chemistry, including benzene rings. So the shapes of snowflakes and the shapes of benzene rings are not totally independent events.