Hugging the globe

I love travel, and given that our family is spread around the world, we frequently fly trans-Atlantic routes to visit each other. On many occasions, sleeplessly fixating on the in-flight TV screen for hours, I have studied the boring channel where our flight's route and progress are depicted on a map of the world. I frequently wondered about the curved shape of the flight route. Why a curve? Wouldn't a straight line be the shortest distance? Sometimes, with no alternative movie channels available, I have contemplated this further, attributing the curvature to the wind direction or mapping from a globe on to a two-dimensional map. It still did not make sense. If globe parallels are drawn as straight lines on a map, why wouldn't flight routes be straight as well?

Equally puzzling is Lindbergh's transatlantic flight route. Why would he, flying solo across the Atlantic on a single seat single engine monoplane, unable to rest his eyes even for a second during the two-day journey, knowing that six of his predecessors have lost their lives along the way, why would he choose anything but the shortest path?


My father resolved this puzzle after his very first trans-Atlantic flight. It turns out that neither of my explanations were fully correct. The shortest distance between two points on a plane is indeed a straight line. However, the earth is spherical. To calculate the shortest distance between two points on a sphere, you could measure a piece of a string that hugs the sphere connecting these two points. If you extend this hug around the sphere you would get a great circle, that cuts the sphere into two halves. Imagine the earth as a watermelon with two marked dots defining our route. Dots can be positioned anywhere, marking two of you favorite world destinations (e.g. Barcelona, New York, Rio De Janeiro.) We can use a wide, long knife to split the watermelon into two halves, slowly cutting through its center and our two route points. The line along this cut on the watermelon's surface is the great circle and the segment between our two points is the shortest path between them. It is a curve hugging the globe, a curve projected onto the map of the airplane's TV screens. A straight line route would be much longer. Charles Lindbergh was very careful to choose the shortest route along the great circle.

I cheer my father, who turns 70 next week: for his curiosity, his optimistic and child-like approach to life, and his joy in the invention and understanding of these little puzzles blossoming everywhere in our life field. And I remind myself to never stop asking questions and searching for answers. Without such quest of mind we would never have known that the earth is a sphere or that big metal machines can fly. If we block our curiosity, we'll never know that other our dreams can come true as well.


Try it at home:
Before taking your next flight, try visualizing your route on the globe. Take a piece of thread and hold one side of it at your departure point and another side at your destination. Pull thread to lie tightly on the globe's surface. The curve made by this thread is your shortest route. Perhaps you can spot something interesting on the way and make an extra stop. Impress your kids and other passengers with this knowledge.

The Math Mom writes about cool, non-intimidating and applicable math of cooking, shopping, parenting, dating, travel and home management. Check out this story: The Math of Your Home Size. Part 1: Make the Best of the Space You Have.