It’s not easy to see, but at the right is a picture of the famous water parabolas at the Detroit Airport. The parabola certainly is a favorite among the fountain designer. I wonder why?
Upon closer inspection, I’m not sure it’s a parabola! Check out my attempt to find the equation of this parabola using Geogebra.
And here is a lovely video of the water feature in action: http://www.youtube.com/watch?v=VSUKNxVXE4E
David Blackwell was a highly-regarded statistician and mathematician who taught at UC Berkeley for 30 years. Apparently he was the kind of mathematician who could become interested in a new topic, learn about it, and then quickly produce profound results. Then he’d move on. Blackwell died on July 8th: his obituary in the NYT can be found here.
Among other things, Blackwell was a strong proponent of the Bayesian approach to statistical inference, and he produced results in Game Theory regarding bluffing and dueling.
Designing a flyswatter is an interesting exercise in 
optimization.
You want it have enough holes so that it can quickly achieve swatting speed, but you don’t want it to have so many holes as to substantially decrease the chance of actually making contact with the pest.
I wonder if there is an industry standard for a flyswatter’s empty-space-to-surface-area ratio.
According to a recent study the default rates for mortgages over one million dollars is nearly twice as high as the default rate for mortgages under one millions dollars (14.3% to 8.3%). A default on a mortgage essentially means that the home-owner stops making mortgage payments and the bank takes possession of the home.
There are a lot of interesting mathematical, sociological, and perhaps ethical questions here, but I wanted to point out that although the above probabilities are interesting, the number and total value of the mortgages in question are probably more relevant data to consider.
For example, if only 1/10 of all mortgages are over a million dollars, then this statistic might not be that important; on the other hand, if a good number of defaults are way over a million dollars, than this statistic isn’t telling the real story either, but in a different way.
As an aside, renting vs. owning is a general and interesting mathematical question to explore in a variety of different contexts.
Paul the octopus must be enjoying his 15 minutes of fame for correctly predicting the outcomes of eight World Cup matches in a row. In fact, a stamp in his honor is currently available at the Shanghai World Expo. This must be a welcome relief from the death threats that followed his [ultimately accurate] prediction of Spain over Germany.
Assuming that the outcome of every match was equally likely (what if you don’t?), then Paul had a 1/256 chance ( that is, (1/2)^8 ) of nailing all eight predictions. That’s roughly a .4% chance, on the order of getting dealt a straight in a five-card poker hand, or rolling a six three times in a row on a fair die. Or, if you prefer, exactly equal to the likelihood of flipping a coin and getting Tails (Arms?) eight times in a row.
Apparently octopi have short lifespans, so it doesn’t look like Paul will be around in 2014 to put his record on the line. At least he’ll go out on top.