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Old 10th Jun 2020, 17:08
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Chu Chu
 
Join Date: Feb 2009
Location: Virginia
Posts: 2,087
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I like to thing about this in one dimension. Imagine you're walking on a road toward a town, and town church bell chimes at exactly the quarter hour. If you're watch is set precisely, you can determine your position on the road from when you hear the bell. If you hear the chime 5 seconds after the quarter hour, you're about a mile from the town (since sound travels about 1000 feet per second).

If you don't an accurate watch, of course, you don't know anything. But imagine the town you just left also has a bell that rings on the quarter hour. If the towns are two miles apart and your hear the chimes at exactly the same time, you're half-way between the towns. And you can set your watch to 5 seconds past the quarter hour. If you hear one chime a second before the other, you're about 500 feet closer to the town with the earlier bell. And with a little simple math, you can work out the time delay from either town and set your watch.

That's just 1-D, of course. But in theory you could work out your position in 2-D with two bells and an accurate watch, or with three bells and no watch. And it would take three bells and a watch or four bells to get a 3-D position. Obviously, the math's harder when you deal with additional dimensions, but the principle's the same.

Last edited by Chu Chu; 10th Jun 2020 at 17:59. Reason: Fixed mistake DaveReid pointed out.
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