Why This 'Curve' is Faster Than a Straight Line w/ Neil deGrasse Tyson

[0:00]Have you ever seen maps of the world and airlines show you their routes between cities? You ever noticed it always makes an arc? It's always a curve. Why don't they make a straight line? You can ask what's the shortest distance between two points on a flat surface? Straight line. But if that surface is curved, it's not immediately obvious what path you should take to minimize the distance travel. That exact path is called a great circle. Let's go from New York to the Middle East. See if we can bring peace to the Middle East. Already done. Since we're used to looking at maps with vertical lines and horizontal lines, you might say, let's just go along the latitude. That's not the shortest distance. The shortest distance is as they say over the pole. Not exactly over the North Pole, but you're going north up here to come down to that. How do we ever figure that out? Here's how you get the great circle. You take the two points and you take a knife and you cut through both points, your origin and your destination. As you cut through the orange in a straight path, that cut must go through the center of the orange and come out the other side. If that cut goes through the center of the orange, then those two points are on a great circle.