PlanetMath: city-block metric

(more info)

Math for the people, by the people.

Main Menu

sections Encyclopædia
Papers
Books
Expositions

meta Requests (197)
Orphanage
Unclass'd
Unproven (498)
Corrections (22)
Classification

talkback Polls
Forums
Feedback
Bug Reports

downloads Snapshots
PM Book

information News
Docs
Wiki
ChangeLog
TODO List
Legalese
About

Entry average rating: No information on entry rating

city-block metric

(Definition)

The city-block metric, defined on $\mathbb{R}^n$ , is

$\displaystyle d(a,b) = \sum_{i=1}^n \vert b_i-a_i\vert$

where and are vectors in $\mathbb{R}^n$ with $a=(a_1,\ldots,a_n)$ and $b=(b_1,\ldots,b_n)$ .

In two dimensions and with discrete-valued vectors, when we can picture the set of points in $\mathbb{Z} \times \mathbb{Z}$ as a grid, this is simply the number of edges between points that must be traversed to get from to within the grid. This is the same problem as getting from corner to in a rectilinear downtown area, hence the name “city-block metric.”

"city-block metric" is owned by akrowne.

(view preamble)

Other names:

city-block distance, taxicab metric

Log in to rate this entry.
(view current ratings)

Cross-references: area, edges, number, grid, points, dimensions, vectors
There are 4 references to this entry.

This is version 5 of city-block metric, born on 2002-01-23, modified 2003-02-23.
Object id is 1552, canonical name is CityBlockMetric.
Accessed 16986 times total.

Classification:

AMS MSC:

54E35 (General topology :: Spaces with richer structures :: Metric spaces, metrizability)

Pending Errata and Addenda

None.[ View all 2 ]

Discussion

forum policy

No messages.

Interact