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Topic: name of a metric
Replies: 21   Last Post: Jul 8, 2007 1:05 PM

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Dan

Posts: 3
Registered: 6/28/07
Re: name of a metric
Posted: Jul 7, 2007 8:28 PM
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[Fernando Revilla]
> P.S. Alternatively I propose the name "Achimota's
> metric" in honour to the first person who asked for it.
> It sounds well and exotic.


I want to say that this metric is _not_ my idea. I found it in Dr.
Timothy S. Norfolk's unpublished paper "When Does a Metric Generate
Convex Balls?" which can be downloaded from his website at
http://www.math.uakron.edu/~norfolk/

It is an interesting paper --- take a look if you have time.

Dan Greenhoe (original poster)

P.S. Achimota is the name of a town in Ghana, West Africa, just north
of the capital, Accra. It is a great place with great people and where
I did have the very great privilege of living for some time some time
ago teaching some math to some high school students. If you want to
name a metric or anything else in honor of the people of Achimota,
that would be great.



On Jul 8, 2:19 am, fernando revilla <frej0...@ficus.pntic.mec.es>
wrote:
> > Does anyone know of a standard name for this metric
> > in R^2?

>
> > d(x,y) = sqrt{ |x1-y1| } + sqrt{ |x2-y2| }
> > where x=(x1,x2) y=(y1,y2)

>
> > Many thanks in advance,
> > Dan

>
> If (x,y) belongs to the intersection B((0,0),1) with the
> first quadrant, then:
>
> sqrt(x)+sqrt(y)<1 <=> x+y+2sqrt(xy)<1 <=> 2sqrt(xy)<1-x-y
>
> <=>4xy<1+x^2+y^2-2x-2y+2xy<=>0<x^2+y^2-2x-2y-2xy.
>
> The boundary related to this open ball in the first
> quadrant is a parabola, so I propose to name this metric,
> "parabolic metric".
>
> P.S. Alternatively I propose the name "Achimota's
> metric" in honour to the first person who asked for it.
> It sounds well and exotic.
>
> Regards.
>
> Fernando.






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