Lines on a Sphere

5. The Alien Baseball Field

Lines on a Sphere

Although Earth is roughly spherical in shape, its curvature does not affect the geometry of, say, a baseball field (diamond) or a network of city streets, because the planet is so large.

NASA

You would have to take Earth's curvature into account, however, if you were plotting an airplane route from Los Angeles to New York and wanted to find the shortest possible path. The standard rules of geometry on a flat surface would no longer apply.

On a small, rounded asteroid, the asteroid's curvature could even affect the shape of a baseball diamond—if the asteroid were small enough.

On a flat surface, the shortest path between two points is a straight line. What is the shortest path between two points on a spherical surface?

TRY IT!

Explore a spherical surface to find the shortest distance between two points.

You will need:

• baseball or tennis ball
• three rubber bands

What to do:

1. Stretch a rubber band around the ball so it makes as large a loop, or ring, as possible.
2. Stretch a second rubber band around the ball at a different angle, again making as large a loop as possible. The two rubber bands should intersect at two different points on the ball. The two points where they intersect should be opposite each other, like the North and South Poles on Earth.
3. Stretch the third rubber band around the ball, again making as wide a ring as possible, and see where it intersects the first two rings. Experiment with putting the third band in different positions to see how it can intersect the first two rings in different ways.
4. Pick any two points where the rubber bands intersect. The shortest distance between them on the ball's surface is along the rubber band connecting the two points.

How to place the rubber bands around the ball.

NEXT: Great Circles and Angles