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It depends on how complicated you want to make it.

The generally accepted answer would be to start at one point, and make a line to the next (a straight line). That's gonna be the answer, say, your teacher might want (sorry if you're an adult :p).

The technical answer? Drill a hole through the globe from one point to the other, and your shortest distance would be the straight line.

Einstein's answer? A geodesic. Look it up :p

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Q: Where is the shortest distance between any two points on the globe?
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