One Million Mung Beans

[Sailboat]

The wife is fantasizing about gathering [pinky in corner of mouth] one million mung beans [/pinky in corner of mouth] as a visualization aid for large numbers.

How much would 1,000,000 mung beans weigh?

How big would the container be?

How much would it cost to buy them in bulk (excluding shipping)?

This is mostly to satisfy curiousity. I once won a contest guessing the number of M&Ms in a 5-gallon jar, but I don’t think I’d be able to guess these answers.

Thanks,

Sailboat

[Green_Bean]

I have to ask…why mung beans?

[Q.E.D]

@Green Bean

I have to ask…why mung beans?

Jealous?

[beowulff]

Surprisingly small.
It seems that an average Mung bean is around 3.4mm in diameter. If we close-pack them, at an average packing density of .74% (from here), we get 1 bean in a cube 4.6mm on a side. That means that 1,000,000 beans would occupy a cube of 100 x 100 x 100, or 460mm on a side, which is around 18"

[Sailboat]

Interesting. But mung beans aren’t exactly spherical…how much would that affect the .74 value?

As for “why mung beans,” I could chalk it up as one of the charms of being married – the other person is an endless source of surprises. But rationally, I think it’s because the dog toys contain mung beans in little rattles, and we’ve been picking a few up after a particularly savage day of toy abuse.

Sailboat

[NurseCarmen]

Who gets to count them?

[Santo_Rugger]

Based on the below cite, I would imagine the ratio would be higher than .74 for the little spheroids.

But M&M’s have developed a whole new group of fans in the science community, and it has nothing to do with how they taste. It seems that M&M’s are a marvel of packing efficiency, and are actually leading to the next generation of design for heat shields and reduced-porosity glass with exceptional transparency.

It seems that the simple act of pouring a bag of M&M’s into a bowl illustrates the propensity of squashed or stretched versions of spheres snuggle together more tightly than randomly packed spheres do. Really, it’s been proven… with bags and bags of M&M’s, and hours of study from talented and dedicated grad students.

<snip>

I suppose it makes sense though, right? Before M&M/Mars got into the act, the human body recognized the efficiency of this particular shape when creating platelets. The component of the blood that must be the MOST efficient at packing together densely to create a blood clot are surprisingly shaped similarly to our snuggly-shaped M&M’s.

Top 10 Scientific Uses For Leftover Halloween Candy

ETA: A more thorough cite shows the number could be as high as .77, but that’s for the M&M shape, so I’d imagine the number for mung beans to be between .64 (random) and .77 (theoretical maximum random efficiency).

In the new research, the scientists considered spheroids – spheres stretched into cigar shapes or squashed into M&M shapes. Stacked neatly, the spheroids still take up 74 percent of the space, just like spheres. But in random arrangements, computer simulations and experiments with M&M’s showed that spheroids could be packed much more densely, filling up to 71 percent of the space.

http://query.nytimes.com/gst/fullpage.html?res=9E03E5DE113AF930A25751C0A9629C8B63

[Santo_Rugger]

Please excuse the double post, this part wasn’t quoted from the second article:

‘‘You can just randomly pour them and without any effort get something that approaches the densest lattice packing,’’ Dr. Torquato said.

The density increases, he said, because ‘‘the particle can move around and rotate to find a more efficient packing.’’

If the spheroids are deformed in a second direction, into ellipsoids (in other words, stretched or squashed so the M&M shape is no longer circular when viewed from above), then the maximum packing density increases to 77 percent, more tightly than the simple neat stacks.

Also, the .64 (random) I refer to is for spheres.

[Santo_Rugger]

Please excuse the triple post.

beowulff, I believe your premise is wrong; we don’t divide 3.4mm by .74, we divide (3.4mm)^3 by 3. The ratio refers to filled versus total space in three dimensions, not in one.

This gives a slightly smaller box size of 14.8", if my math is correct:

(3.4mm)^3/.74 * 1000000 = 53.11e-3m^3

(53.11e-3m^3)^(1/3) = 376mm

376mm = 14.8in