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I'm trying to come up with a rationalisation for using the Euclidean distance in an application of mine. Any thoughts on why it is the fundamental choice?

Thanks

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    I am not sure whether I understand your question. The Euclidean distance is the "normal distance in the real world". In other words, if you take a ruler and measure the distance between two points, then it's the Euclidean distance.2012-08-21
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    Is there another metric you're considering?2012-08-21
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    At the moment it sounds like you want to rationalize it *because you want to use it*. Shouldn't you rationalize it because the evidence indicates it is the best choice? If that is the case, then we need information about your application, so we can reason that it is the best choice.2012-08-21
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    I guess I was considering (sum(i=1 to n) (xi - yi)^k)^(1/k) where k=2 is the standard.2012-08-21
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    This is a very good question. I don't understand why it got downvoted.2012-08-21
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    I would suggest that you migrate the question to http://physics.stackexchange.com/ I agree with Christian Blatter that the question is good, but (*some*) mathematicians don't like questions about why something is natural in relatino to the real world. However, maybe physicists would be able to say more about finding distances in the real world and why the Euclidean metric is "natural". From what I understand, this might actually not be the case when you look out into all of space.2012-08-21
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    If the situation naturally fits the metric then there's no reason to "come up with" a rationalization. Inventing a rationalization without appealing to the situation seems dishonest. There *probably are* such reasons the OP has in mind, so I wish @conor would let us in on them.2012-08-21
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    @Thomas I don't think this question has any relation to physics at all - indeed, my first presumption was that it was closer to a fitness measure for statistical applications! I think this is a perfectly natural question here.2012-08-21
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    @StevenStadnicki: You are probably right. It is still not clear to me though what the OP is asking about. He hasn't said anything about the "application" of his. As to the general question about why the Euclidean metric is *the* natural choice, I would still say that might be better answered in physics.2012-08-21
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    @Conor: I don't understand the question. Depending on the application, it may _not_ be the natural choice. What is the application?2012-08-21
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    [Cab drivers beg to differ](http://en.wikipedia.org/wiki/Taxicab_geometry).2012-08-21
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    A better formulation of this question might be: "Under what conditions is the Euclidean metric the best choice and why does this set of conditions prevail in such a diverse set of applications."2013-12-07

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