* Here in El Salvador, whenever people need to cut a round cake, they first cut a circle in the middle of the cake. And then they proceed to slice the outer rim of the cake into equal slices. When they serve, first they serve the slices on the rim, and then they serve the center piece last.
A natural math question that arises from this is: How big will the middle piece have to be, in order to ensure that all of the pieces served are of the same size?
The math is very easy, so I'll leave it to you to figure out. I'm going to give it to my Geometry kiddies at some point, as a warmup problem. (Of course, the kids will have to figure out for themselves that the answer will depend on N, the number of slices, and R, the radius of the cake.)
On a random note: I like how they cut it this way. It actually makes sense to me, because it's much easier to serve the slices when they're not all long and skinny.
* Also, another amusing custom here is that when Salvadorans have a really big raffle prize (ie. Taca's round-trip tickets at today's staff luncheon at our school), they often will announce something like, "We're going to pick 3 names. The first and the second people we pick out of the hat do not win any prize; their names get discarded on the side. The third name we pick out is the sole winner."
It's funny because it's clear that this does not change the probability of winning. Each person still has the probability of winning = 1/n, whether you compute it as a one-time pick of a single name OR as the consecutive-picking-of-three-names-without-replacement method as described above: (n-1)/n * (n-2)/(n-1) * 1/(n-2) = 1/n. But the Salvadoran way is much funnier. The first two names picked out of the hat are the sorest losers (or they go around and brag about how close they had come to winning). How funny!!
...I love how there is math everywhere! :)
Anyhow, I am on vacation now, and will very likely be a useless lump until January. See you then.
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