SMMG
"Oranges in a box, and other stories"
featuring Alice Mark
Video (sound comes in at 9:05)
On January 19, 2014, to kick off a new season of UT Austin's Sunday Math Circle, we spent an afternoon playing with the shape our group is named for. Graduate student Alice Mark gave us a taste of the deep and intricate math hidden in a simple-sounding task: packing coins, oranges, and other circular objects into boxes.
We started out working in small groups, trying to pack as many pennies as we could onto a quarter-size sheet of paper. The two most popular strategies both arranged the pennies in a regular pattern: a square grid, like a checkerboard, or a triangular grid, like a honeycomb.
After comparing some popular strategies, we examined our packings mathematically, calculating the fraction of the paper we'd managed to cover with pennies and counting pennies' nearest neighbors. Then we started thinking about idealized square and triangle packings; we counted nearest neighbors and found the fraction each packing would cover of an infinite plane. (Of course, we had to figure out what it means to "cover a fraction of an infinite plane" first...)
When we got tired of pennies on planes, we moved up into the next dimension. We played with different ways of stacking oranges, which turned out to be a lot more complicated than the penny arrangements we'd been investigating.
