Talk:Distance

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Could somebody who knows how please write out the distance formula in symbols, too, just for clarity? I read the last paragraph a couple of times before I realized that it was talking about the formula I know :) Dreamyshade

I split proxemics and propinquity into separate articles. When people are looking for 'proxemics' they will likely be surprised to see a page about geometrical distance. Ditto for 'propinquity' -- I study both mathematics and psychology, and propinquity is a major topic in social psychology, but I have never heard it used in geometry.

--Johnkarp 11:11, 9 Oct 2004 (UTC)

Contents

[edit] removed not well-explained and unhelpful paragraph

I removed the following text from distance

Distance is one sort of interval between things or events, Time being the other.

I found it unclear. Oleg Alexandrov 22:20, 31 May 2005 (UTC)

But see Time. Banno 21:39, May 31, 2005 (UTC)

OK, you are writing at the very beginning of the time article:

Time is one sort of interval between things or events, distance being the other..

I am not sure this is a proper characterisation of time. I am not sure time and distance can be compared in that way. I am not sure you what you mean by interval in this sentence. I cannot even say that what you wrote is incorrect, I think it is ambiguous and confusing. Would you clarify me please? Oleg Alexandrov 22:14, 31 May 2005 (UTC)

An excellent point - I see the circularity in interval. I had just retained the word from a previous edit. Try:
Time is one sort of separation between things or events, distance being the other..
Failing that, I'm open to your suggestions. Banno 22:48, May 31, 2005 (UTC)
This sentence is true. But I do not think it is so important or so releveant as to be the very first sentence in either the distance article or in the time article. Oleg Alexandrov 23:37, 31 May 2005 (UTC)
If you wish to demote it, be my guest. But then, what is your suggestion for an introduction to time? The advantage of this sentence is that it draws attention to the link between time and distance; it is also succinct. Banno 23:48, May 31, 2005 (UTC)

[edit] Reworked Article

I’ve made some rather significant changes to this article. In the course of doing so, I deleted the following material. Wherever possible, I’ve attempted to reincorporate this information elsewhere in the text, but some of it didn’t seem particularly pertinent to the discussion. As this is one of my first attempts, I would appreciate feedback from more experienced users. It would be nice if someone could help with the page layout or say something more about physics and informal treatments. I wasn't sure what to do with the "Euclidean spaces" section either, but it seems a like it might be a bit excessive for this article.

The distance between two points is the length of a straight line segment between them.
Sometimes a distance thus indicated is ambiguous because the means of transport is neither mentioned nor obvious.
In the study of complicated geometries, we call the most common type of distance Euclidean distance, as we define it from the Pythagorean theorem.
===The distance formula===
The (Euclidean) distance, d, between two points expressed in Cartesian coordinates equals the square root of the sum of the squares of the changes of each coordinate.
Thus, in a two-dimensional space
d = \sqrt{(\Delta x)^2 + (\Delta y)^2},
and in a three-dimensional space:
d = \sqrt{(\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2}.
Here, "Δ" (delta) refers to the change in a variable. Thus, Δx is the change in x, pronounced as such, or as "delta-x". In mathematical terms, \Delta x = \left|x_1 - x_0\right|, and so (Δx)2 = (x1 − x0)2.
This distance formula can be seen as a specialized form of the Pythagorean theorem; it can also be expanded into the arc-length formula.
== Formal definition ==
A distance between two points P and Q in a metric space is d(P,Q), where d is the distance function that defines the given metric space.
We can also define the distance between two sets A and B in a metric space as being the minimum (or infimum) of distances between any two points P in A and Q in B.
Alternatively, the distance between sets may indicate "how different they are", by taking the supremum over one set of the distance from a point in that set to the other set, and conversely, and taking the larger of the two values (Hausdorff distance).
===Generalized distance in arbitrary dimensions: Norms===
== Distances in other spaces ==
==Distance covered==

--Fell Collar 06:39, 10 March 2006 (UTC)

Headers should have sentence-style capitalization (i.e. only one capital).
Also you made some odd deletions, e.g. in the section on the distance between sets.
Please do not start a line with a blank space, even on the talk page, it makes lines wider than the screen.--Patrick 14:38, 10 March 2006 (UTC)
I've put back the material about the Hausdorff metric in the section on distance between sets and fixed the headers. Are there any other deletions that struck you as inappropriate? I had read that it is considered polite to move deleted material to the talk page, but I wasn't sure how to format it. What is the convention? --Fell Collar 16:51, 10 March 2006 (UTC)
Aw, I see it right above: indent and italicize. I've restored a great deal more of the material I'd deleted. In retrospect, I'm not sure why I got rid of a lot of it. The remainder is either
  • paraphrased elsewhere in the article
  • a now-defunct header, or
  • superfluous (e.g. the bit about "delta x", which should be fairly obvious from the way I've formatted the equation)
Fell Collar
Thanks!--Patrick 00:32, 11 March 2006 (UTC)

[edit] Negative Distance?

Someone (81.207.214.244) indicated that one could have negative distance if it was "predefined". I wonder if they (or someone else) could elaborate. If distance was negative, it certainly wouldn't be a metric, so it seems odd to me that we would call it "distance" in a formal setting. Can someone give an example? --Fell Collar 18:03, 13 March 2006 (UTC)

I'm moving the sentence here for now. It seems very suspect, and at any rate distance certainly won't be negative in Euclidean space (the section it was placed in). If someone could elaborate and put this where it belongs, that would be nice.
There is no such thing as a negative distance (unless it is predefined).
--Fell Collar 03:41, 16 March 2006 (UTC)

Ive changed the heading of what was the physics section, because, it appeared to have nothing much to do with physics! I made a new physics description, and put it at the top, but I think it generally covers what most people know of as distance. I deleted the "distinctions" of distance that had been written, that said things like "the distance formula is not true for curved surfaces", which cant be true, because the distance formula is part of the law of physics and is always true! they were true in a general sense, but i didnt see how they had any useful meaning.

if someone understands the special theory of reletivity better than i do, can they please give some information on how distance applies generally in physics.

ive been thinking that it might be overkill to seperate this topic into physics/geometry/maths, because distance is all of them at once, and it doesnt need to be explained over and over in slightly different senses.

[edit] physics

It's amazing that there's so little on physics in this article. Physical distance is a pretty important concept in that field. Michael Hardy 05:04, 18 December 2006 (UTC)

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