There are an estimated 20,000 to 25,000 polar bears in the world, and the population is expected to decline by 30 percent over the next three generations. Periscopic, in collaboration with the Polar Bear Specialist Group, highlighted the changing populations in this interactive.

The data can be viewed by subpopulation, by nation, and by ecoregions. In the first two views, you can click on geographic regions to see more details about the area, which includes a text overview and time series for more troubling numbers on polar bears killed by humans and pollution. Finally, when you click on a time series or the pollutant levels, you can see the data at a higher granularity.

So there are a few ways to examine the data and different angles to explore. You’ll want spend some time with this one.

I’m not sure where this is originally from, but I found it on an intro to geology course page. What happens when midnight comes around again?

As you’ve probably heard, Apple and Samsung have been in a bit of a kerfuffle over the past few months. We own that patent for that thing. No, we have this patent for that. The state of technology patents is all over the place. The New York Times takes a closer look. Also, don’t miss the video and side-by-side comparisons.

How many people does it take for there to be a 50% chance that a pair in the group has the same birthday? Only 23 people. What about a 99% chance? Maybe even more shocking: 57 people. This is the birthday problem, which every undergrad who’s taken a stat course has seen. Steven Strogataz explains the logic and calculations.

Intuitively, how can 23 people be enough? It’s because of all the combinations they create, all the opportunities for luck to strike. With 23 people, there are 253 possible pairs of people (see the notes for why), and that turns out to be enough to push the odds of a match above 50 percent.

Incidentally, if you go up to 43 people — the number of individuals who have served as United States president so far — the odds of a match increase to 92 percent. And indeed two of the presidents do have the same birthday: James Polk and Warren Harding were both born on Nov. 2.

The Johnny Carson clip referenced in the article is worth watching. Carson tries to test the results with the audience, but goes about it the wrong way.