Faster Algorithm for Sphere Packing Discovered

sciencehabit writes with an article in Science about a new way to pack spheres into a cylinder. From the article: "One day, physicist Ho-Kei Chan of Trinity College Dublin was playing with steel ball bearings, trying to pack them into a little cylindrical tube in the most efficient way possible. It's a tricky problem that can take even a powerful computer a week to calculate. But after thinking about it for a while, Chan has figured out a way to simplify the math. The advance could help engineers pack all sorts of spheres more efficiently, from nano-sized buckyballs to Christmas tree ornaments. Another potential application is liquid crystal displays such as those used in televisions and computer monitors. If scientists could make liquid crystal molecules obey these rules, they could potentially create a whole new class of liquid crystals." One caveat is that the diameter of the cylinder can be at most 2.7013 times as large as the diameter of the spheres being packed.

Comments

Innovation!

[Anonymous Coward]

Scientist finds new innovations while playing with balls. News at 11.

Had to be asked.

[sgt scrub]

Do you really need math to properly pack balls?

Re:Had to be asked.

[BigMike]

I'm not dumb, but can you provide an example using pancakes?

Re:Had to be asked.

[Ibiwan]

Yes. To simplify the math, assume the pancake is a sphere...

The math is even simpler

[Anonymous Coward]

If the diameter of the cylinder is at most 1.0000 times larger than the diameter of the spheres being packed.

Re:The math is even simpler

[pnewhook]

The math gets really simple if you solve it as an Engineer. The highest packing efficiency and theoretical maximum density can be clearly shown to be achieved if the volume of the spheres added is equal to the volume of the container itself. This can be shown for any number of spheres of any diameter and any size container, assuming no one sphere is bigger than the container itself. The practical engineering solution then gets applied by heating the container so the spheres melt and form a liquid, thus achieving the theoretical maximum packing density.

Take that math nerds. Boo yeah.

Re:Interesting

[ArsenneLupin]

But wouldn't shaking the cylinder empty the balls?

Re:For those of you wondering

[pnewhook]

I suppose I should expect some irrational number expressed as a power of some rational number to pop up, but 5 seems like such an innocuous number

Because 5 is the number of points on a pentagram which is the sign of the devil. Any math with 5 or sqrt(5) should be avoided at all costs lest the devil take your soul and you are then stuck being an accountant.