# More Math and Vegetables

I picked the wrong pot while preparing potatoes, and found the pot a little full.

I had to slice up the potatoes into smaller chunks so that they could all fit in my pot.  Predictably, my poorly planned pot of potatoes prompted me to ponder the packing problem.

In a simple form, the packing problem asks “What’s the best way to pack oranges in a rectangular box?”  Should the oranges be in columns (sitting right on top of each other?), or should you try to fit oranges into the gaps created when you make an orange-square (more like a pyramid?).

The packing problem, despite its seemingly modest statement, leads to very complicated and deep ideas.  My potatoes led to a very delicious side dish.

#### patrick honner

Math teacher in Brooklyn, New York

#### Kevin Hung · October 12, 2010 at 8:05 pm

just a thought…
I don’t know if you can see this but.
Let’s say you pack into the gaps..
you probably have
O O O O O
O O O O
O O O O O
Assuming that the ORANGE isn’t big enough to fill the left most and right most gap, you have 4 oranges in the middle, not only that, consider it to be in a 3 dimensional form, you probably will lose the whole outer surface area of oranges where as if you put it into columns form… Unless… the “height” of the box is perfectly suitable for the “GAP filling” image I had provided(as in only 2 columns if i fill that box with oranges and having a few inches empty on the height), I believe that the column method would be better off?

Correct me if I’m wrong because afterall, I found this quite fascinating how all “fruit” farms pack their fruits in columns and not in gap filling methodology.

#### Ahmed Gouda · October 15, 2010 at 4:59 pm

Technically, it would be better to avoid stacking in pyramid form, but instead have the oranges on top of each other directly (Way harder to do..) The reasoning is this:

O 0 0
O O < 0 0

#### Ahmed Gouda · October 15, 2010 at 5:02 pm

Ahmed Gouda :
Technically, it would be better to avoid stacking in pyramid form, but instead have the oranges on top of each other directly (Way harder to do..) The reasoning is this:
O 0 0
O O < 0 0

Well it looks like the comments doesn’t like 2 spaces next to each other. Basically, a rectangular prism has a higher volume then a Pyramid, and even if it isn’t going to have a pointy top, the pyramid will still have a smaller area with every other “Layer” of oranges compared to just having it right on each other…of course, like I said. That would be so much more hassle. It’d involve balancing oranges…

But then if I think about it, just putting them in where you can might be better. Just avoid leaving gaps that are smaller than an orange, but still pretty large as best you can?

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