This is in a textbook:
The area of a washer is pi*R^2-pi*r^2, which you can simplify to pi*(R^2-r^2), but not to pi*(R-r)^2. No matter how tempting it is to make the latter simplification, it’s wrong. Don’t do it.
Quoting from the math subreddit:
“Proof — easy numeric comparison. There are 52! possible orderings of a deck, and I’m assuming all are equally likely after your shuffling. Let’s wildly overestimate and assume that every second since the universe was created, a million decks of cards were shuffled and someone looked through them. Thus fewer than 10^24 orderings have ever been seen.
But at an incredibly crude estimate, 52! is at least 10^42 * 10!; let’s underestimate that again wildly by 10^42. That means that chances of your ordering ever having come up previously are at most 1 in 10^18.
(Note, by the birthday paradox, the chances that there have been two identical orderings observed by two people in history are quite a bit higher — perhaps even feasibly likely; I haven’t calculated it. But we’re looking here at the probability that a given ordering matches one of the ones previously seen.)“
This is pretty funny (via the consumerist).
Comcast sent a letter to this guy named Aaron demanding he pays -$0.05 to avoid interruption in service.
This is old but curious nevertheless:
Seems that Wellesley College is an all-girls college? Some insight into the origins of the graph.