Talk:Distance

message: 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)
thread_title:  (old) 

message: Please see Talk:Metric (mathematics)#Content syncronizing. `'Míkka 17:52, 8 October 2007 (UTC)
thread_title:  Content syncronizing 

message: I am of the opinion that a section on distance between 
functions be added:
For e.g. In the fourier series representation of a simple 
periodic function f(t) with time 't' as the independent 
variable, the fourier coefficients are so adjusted that the distance between the finite fourier sum and the function f(t) is minimized.
Here the distance between f(t) and g(t) is given by :
{(1/2pi integral((f(t)-g(t))sqrd.dt}sq. root.
It would be infromative if this is discussed in the article.
Sridhar10chitta (talk) 08:48, 27 November 2007 (UTC)
thread_title:  Distance between functions 

message: It would probably be appropriate if a section describing the distance of a time dependent function maybe f(t) = at^sq + bt +c is added as well before discussing the distance between functions.
Sridhar10chitta (talk) 16:56, 28 November 2007 (UTC)
thread_title:  distance of a function 

message: This article mainly talks about distance in mathematics.  Most of that material is in Metric (mathematics), or could be moved there.  There is little mention of distance in physics, and no mention of distance in everyday use.  Why do we have this article? --Taeshadow (talk) 15:49, 11 March 2009 (UTC)
thread_title:  Purpose of this article 

message: The Euclidean distance between two objects may also be generalized to the case where the objects are no longer points but are higher-dimensional manifolds, such as space curves. Additional concepts such as non-extensibility, curvature constraints, and non-local interactions that enforce noncrossing then become central to the notion of distance. The distance between the two manifolds is the scalar quantity that results from minimizing the generalized distance functional, which represents a transformation between the two manifolds:
: 
\mathcal {D} = \int_0^L\int_0^T \, ds \, dt \left \{ \sqrt{\left({\partial \vec{r}(s,t) \over \partial t}\right)^2} + \lambda \left[\sqrt{\left({\partial \vec{r}(s,t) \over \partial s}\right)^2} - 1\right] \right\}
If two discrete polymers are inextensible, then the minimal-distance transformation between them no longer involves purely straight-line motion, even on a Euclidean metric. There is a potential application of such generalized distance to the problem of protein foldingSS Plotkin, PNAS.2007; 104: 14899–14904,AR Mohazab, SS Plotkin,"Minimal Folding Pathways for Coarse-Grained Biopolymer Fragments" Biophysical Journal, Volume 95, Issue 12, Pages 5496–5507
This generalized distance is analogous to the Nambu–Goto action in string theory, however there is no exact correspondence because the Euclidean distance in 3-space is inequivalent to the space-time distance minimized for the classical relativistic string.
:OK. I added a section on variational formulation of distance. This will make the above text much more accessible to an non-expert user. Nocompletechaos (talk) 07:42, 26 September 2009 (UTC)
thread_title: Generalization of Euclidean distance to higher-dimensional manifolds

message: Currently the article begins:
:Distance is a numerical description of how far apart objects are.
Sometimes distance is not expressed numerically, but rather quantitatively as in "A is further away than B". Also, sometimes it is not about how far apart objectS are, but about how extensive a single object is - either numerically as "A is 3 metres long", or non-numerically (but still quantitatively) as "A is taller than B". It can aso be the distance travelled in a period of time, like "The Earth travels further in one orbit than Mercury does"   JimWae (talk) 09:28, 12 July 2010 (UTC)
thread_title:  Definition 

message: What's the definition of prudent distance? I saw it in an article about Cassini's final days and said 'Cassini is orbiting Saturn at the same inclination it will have during the Grand Finale, but at a more prudent distance.' I learned the definition of prudence but how that relates to distance? PlanetStar 00:32, 28 April 2017 (UTC)
replies: text: This is not a technical term, which is probably why no one has responded to your query. Some editor was just waxing eloquently when what was meant was a "safer" distance, that is, not so close as to spiral into Saturn as it will during the Grand Finale.--Bill Cherowitzo  (talk) 04:26, 13 May 2017 (UTC)
thread_title:  Prudent distance 

message: Is there any source for the definition given?131.114.35.40 (talk) 14:11, 26 October 2022 (UTC)
thread_title:  Definition source 

message: Distance 2001:4456:1C3:4A00:FCE1:8FD8:B7B4:7564 (talk) 10:48, 1 February 2023 (UTC)
thread_title:  Science 

message: What is Distance 122.52.249.56 (talk) 12:44, 8 January 2024 (UTC)
thread_title:  Science