Dan
Posts:
3
Registered:
6/28/07


Re: name of a metric
Posted:
Jul 7, 2007 8:28 PM


[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 Timothy S. Norfolk's unpublished paper "When Does a Metric Generate Convex Balls?"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{ x1y1 } + sqrt{ x2y2 } > > 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)<1xy > > <=>4xy<1+x^2+y^22x2y+2xy<=>0<x^2+y^22x2y2xy. > > 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.

