Did you know that the Senate recently heard testimony on a bill that might lead to Puerto Rico becoming the 51st state? Apparently the Puerto Rico Democracy Act of 2010 already passed in the House and could allow residents to decide on the island's political status. Upon learning of this hypothetical new state, Chris Wilson of Slate wondered how we would go about adding another start to our flag?
I put the question to mathematician Skip Garibaldi, who did what anyone would do in this situation: He wrote a computer program to figure out all possible combinations for flags of any number of stars. To do this, he looked at all the flags we've flown throughout American history, found the most common patterns, and figured out which of those patterns worked for a given number of stars.
Then Slate used Garibaldi's code to build an interactive flag calculator, which is really quite fun. The analysis that follows—on various types of symmetry—is pretty awesome, too. If you're into that sort of thing.