This blows my mind:
In North America, some Muslims pray to the northeast, in the direction of the great-circle route (the shortest path along the planet’s surface) to Mecca, whereas others pray to the southeast.
From an article with a winking title: A sine on the road to Mecca.
If I was Muslim, I think I’d pray to the northeast. It’s counterintuitive, but it’s pretty amazing to imagine a prayer shooting out of your mind and blazing through the cold Arctic reaches on its way to the sweltering kaaba.