This week's episode in Steven Strogatz's series Math: From Basic to Baffling is on differential geometry: Think Globally. While I leave it to you to read the article for all the good stuff -- and videos! -- about the shortest path between two points on curved surfaces, I want to excerpt something that makes this series truly great:
Sometimes when people say the shortest distance between two points is a straight line, they mean it figuratively, as a way of ridiculing nuance and affirming common sense. In other words, keep it simple. But battling obstacles can give rise to great beauty — so much so that in art, and in math, it’s often more fruitful to impose constraints on ourselves. Think of haiku, or sonnets, or telling the story of your life in six words. The same is true of all the math that’s been created to find the shortest way from here to there when you can’t take the easy way out.
Two points. Many paths. Mathematical bliss.