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Closed-path temperature
Jun. 25th, 2012 03:32 pmHere's an interesting example of how certain ideas from math apply to other fields in ways that might not be expected.
Suppose you draw out a loop path on a map. Any map you want; any shape path you care to draw, as long as it starts and ends at the same point.
Is it possible that every location along the path you drew is a different temperature? Or must there be at least two locations on that path that are the same temperature? Why?
(Clarification: when I say "location on the path" I mean locations in the actual place represented by the map--but that doesn't actually matter; if we were instead discussing the temperature of different parts of the map itself, it would still be fundamentally the same question.)
Suppose you draw out a loop path on a map. Any map you want; any shape path you care to draw, as long as it starts and ends at the same point.
Is it possible that every location along the path you drew is a different temperature? Or must there be at least two locations on that path that are the same temperature? Why?
(Clarification: when I say "location on the path" I mean locations in the actual place represented by the map--but that doesn't actually matter; if we were instead discussing the temperature of different parts of the map itself, it would still be fundamentally the same question.)
