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From: Valentin Samko (boost_at_[hidden])
Date: 2004-11-06 19:26:26

MW> The word I was looking for is "Ortsvektor" in German, the vector from
MW> the origin to a certain point. What would be the proper word for that
MW> in English (tried googling, failed :)?

I do now know any other english term for that except for a "vector",
but I am not a native english speaker as well.

MW> The Euclidean space is E^3, the vector space is R^3.
MW> Please see:
MW> Note also: "Not all books make this distinction so you need to be
MW> prepared to encounter the unstated identification E^3 = R^n"
MW> Mathworld is using this _unstated_ _identification_; it is imprecise at least.

It's not just Mathworld, it's thousands of books/articles. In any
case, don't we assume, the gui library will use R^2 space?

>> In C++ sence - yes, it's a different point. In mathematical sense,
>> point-point depends on how this operation is defined in your
>> particular space, and in Euclidean space, the result of this
>> operations is the same as difference of corresponding vectors.
MW> Yes. But the result is a *vector*. IOW, the difference between 2
MW> points is a mapping from two points in Euclidean space to a vector in
MW> a vector space:
MW> difference :: E^n x E^n -> R^n
I just do not get this. Why would you have a difference between two
points in E^n defined as a point in R^n?

Valentin Samko

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