Talk:Chebyshev distance

Chebyshev?

When was this L-infinity distance first called Chebyshev distance? I don't think this usage is common at all. Was this coined in the last 20 years or so? It evidently was not listed as such in the Cantrell book cited as a reference from 2000. Chebyshev was an excellent mathematician no doubt, but I'm not sure he had any particular impact on the L-infinity norm. 207.140.43.81 (talk) 01:43, 18 January 2019 (UTC)

I'd also like to see a source for this name. Jamgoodman (talk) 20:25, 14 April 2019 (UTC)

A good question for a wikipedian, but to doubt that Chebyshev had anything to do with distances is ignorance and scientific laziness, unbecoming of wikipedians. He did invent his distance, more precisely he invented Chebyshev norm, which, of course he did not call so. Unfortunately mathematicians are scarse in wikipedia, so this subject is in a sorry state. Still, an interesting quest remains, to firure out who (re)named it or at least to find earliest usages.- Altenmann >talk 00:46, 15 April 2019 (UTC)

The oldest reference using this name (under either "Chebyshev distance" or "Tchebychev distance") that I can find online is John, Fritz (1952), "On integration of parabolic equations by difference methods. I. Linear and quasi-linear equations for the infinite interval", Communications on Pure and Applied Mathematics, 5: 155–211, doi:10.1002/cpa.3160050203, MR 0047885. But there may be older in the Russian-language literature. —David Eppstein (talk) 01:18, 15 April 2019 (UTC)

This ref is about the distance betweem functions, ie basically about chebyshev norm. russian refs prefer the term "чебышевская метрика" (chebyshev metric) . Unfortunately earliest digitizet text I found dates 1962. Interestingly, I saw one early article (but not so early) which says that "foreign authors use this term more frequently than the Soviet ones". So I guess we beter start looking for German and French refs, with all transliterstion horrorrss; Tschebyscheff and the likes.

Tschebyschev himself used the term " максимальное уклонение" (literally, maximal deviation), which term is used by russians in tjis context until now. By the way, Chebyshev polynomials artickle fails to mention the historical fact tnat T_n() polynomials originated from the problem Chebyshev was dealing with originally, namely, approximation of function wuth polynomials, the refined version being to find the nth degree polynomial with least "maximal deviation from zero" (i.e.chebyshev norm.) on segment [-1,1]. - Altenmann >talk 05:23, 15 April 2019 (UTC)

P.S. Browsing around, I started favoring Jitse Niesen's 2007 #Assessment comment/merge suggestion. Because now chebyshev metric redirects here, thus compLeteLy missing the prevailing usage of the term in approximation theorry. Would you support it? - Altenmann >talk 05:58, 15 April 2019 (UTC)

For what it's worth Scipy (a very popular scientific computing library) uses this name; https://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.distance.chebyshev.html#scipy.spatial.distance.chebyshev --Phissy (talk) 16:25, 26 August 2020 (UTC)

A modern name should be used. See below. LMSchmitt 03:16, 13 November 2020 (UTC)

Untitled

Please explain the terms in the equation. --JDitto

please explain the whole thing...--Ioshus^(talk) 03:05, 3 January 2007 (UTC)

its a way to calculate distance. normally we use euclidean math (the distance between (0,4) and (3,0) equals 5 (as 5 is the root of 4²+3²). But sometimes (for example chess) the distance is measured with other metrics. On a chess board the distance between (0,4) and (3,0) is 3. --81.82.213.211 (talk) 15:49, 31 January 2011 (UTC)

no. it's 4.

a circle is defined by a collection of points who are on a same distance from a center point. If you look at the chess map, and take all the squares with distance 2 from the king, you get a square figure. --81.82.213.211 (talk) 15:49, 31 January 2011 (UTC)

This is great, I've used this for years but didn't know there was a name for it. Can someone add a pronunciation?--74.251.60.244 (talk) 22:20, 6 September 2009 (UTC)

Concerning the L_p metrics: $\lim _{k\to \infty }{\bigg (}\sum _{i=1}^{n}\left|p_{i}-q_{i}\right|^{k}{\bigg )}^{1/k}.$ If it's called $L_{p}$, the limit shoudln't go over $k$, but over $p$. I know this interferes a little with the $p_{i}$, but still. -- 129.27.201.116 (talk) 15:31, 6 June 2011 (UTC)

Fixed; in less than 8 years.I guess nobody could find a WP:RS for it. :-(.- Altenmann >talk 06:09, 15 April 2019 (UTC)

Using $x$ and $y$ as names for two different vectors is VERY confusing. Actually, it's just plain wrong. $x_{i}$ and $y_{i}$ imply the x-axis and y-axis components of the same vector. Two different vectors should never be given the symbols $x$ and $y$, especially when we're talking about 2D space. — Preceding unsigned comment added by 198.53.211.7 (talk) 20:46, 8 October 2020 (UTC)

I don't think so this is equal to Chessboard distance

I am testing this and Chessboard distance and get different results.
I tested by using http://accord-framework.net/docs/html/M_Accord_Math_Distance_Chessboard.htm vs http://accord-framework.net/docs/html/M_Accord_Math_Distance_Chebyshev.htmBurstPower (talk) 11:39, 3 March 2016 (UTC)

Example: King's shortest path from (1,1) to (3,6)

,_,_,_,_,_,_,_,_,_,_,

,_,_,o,_,_,_,_,_,_,_,

,_,_,o,_,_,_,_,_,_,_,

,_,_,o,_,_,_,_,_,_,_,

,_,_,o,_,_,_,_,_,_,_,

,_,o,_,_,_,_,_,_,_,_,

,o,_,_,_,_,_,_,_,_,_,

This has 5 steps, the largest component of the point (2,5)=(3,6)-(1,1). Strategy: always run diagonal towards the other point. Then stay on the same row or column. Above: 3 steps up. LMSchmitt 10:52, 15 November 2020 (UTC)

The leading word describing this norm should be $L^{\infty }$-norm or sup-norm

That are the standard terms used in math. Chebychef-norm should be mentioned of course. But books such as functional analysis books that seriously deal with such norms use $L^{\infty }$-norm or sup-norm. https://www.amazon.com/Functional-Analysis-Walter-Rudin/dp/0070542368.LMSchmitt 03:12, 13 November 2020 (UTC)

I wholeheartedly agree. Calling what every high-schooler knows as the infinity norm the "Chebyshev norm" is just plain obfuscation. 2A01:CB08:895:F000:329C:23FF:FEA2:DF4F (talk) 17:38, 29 October 2022 (UTC)

The infinity norm is for function spaces, not for finite-length sequences, which is what this article is about. Related concepts, but not the same. Perhaps this should be explained more clearly. 67.198.37.16 (talk) 00:17, 26 November 2023 (UTC)

Assessment comment

The comment(s) below were originally left at Talk:Chebyshev distance/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

Article should be more clearly delineated from uniform norm or merged. -- Jitse Niesen (talk) 08:17, 21 May 2007 (UTC)

Last edited at 08:17, 21 May 2007 (UTC). Substituted at 19:51, 1 May 2016 (UTC)