Learning math consists of mastering basic concepts and using them as building blocks to understand more complex ideas. A good way for students to understand these ideas is to apply them to the real world. This starts far earlier than you might realize. Even before they go to school every child – especially those with siblings – understands the concept of greater than or less than. As proof give one child three cookies and her brother only one and see how long it takes for chaos to ensue.
Another one of the earliest concepts we all learn is the idea that the shortest path between two points is a straight line. Children learn by measuring distances between points on a piece of paper with and without an intermediary third point that lies off the straight path. They quickly master the concept and apply it to maps. It’s ingrained in most of our brains. We understand ‘as the crow flies’ implies an obstacle stands between us and the straight path to our destination.
I recently used this concept to help swimmers understand the importance of good swimming technique. They may not get the bio-mechanics, but ask them if they’re faster swimming in a straight line or zigzaging down the pool and they immediately grasp the idea.
Last week’s post included a brief mention of a gravity train which falls through the center of the Earth to reach the antipode of its starting point, i.e., it takes a straight line path between the two points. Unfortunately, the gravity train is purely theoretical. In the real world we travel along the surface (or near it) of the Earth, which as we all know is not flat. The shortest path between two points on the Earth is along a great circle route. That’s a circle whose plane slices through the center of the Earth. In other words it splits the world in half.
Today’s Map
The map below is an example of the longest segment of a great circle path that you can travel over water. It covers ~20,000 miles from Pakistan to Kamchatka.
The distortions of projecting a three dimensional curved surface onto a two dimensional screen gives the line it’s curvature. You could certainly verify that with a desktop globe. For those of you wishing for the easier proof here’s a cool video.
The longest great circle path you can travel without swimming can be found at Guy Bruneau’s web site.
As always, thanks for reading.
Armen
Cool.