Re: Thinking about metric spaces

In article
<6441796.1183148156554.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
tommy1729 <tommy1729@xxxxxxxxx> wrote:

In article
<1182926935.206647.132790@xxxxxxxxxxxxxxxxxxxxxxxxxxxx
,
bit188 <mariana@xxxxxxxxxxxxx> wrote:

Another question: what other kinds of metrics are
there?

Take any convex set in R^2 (or R^n), symmetric with
respect to
the origin, and declare that for all points on the
boundary of that set
the distance to the origin is 1. Then to find the
distance between
any two points move a copy of your convex set so its
center is at
one of the points & see how much you have to scale
the set so
the other point is on the boundary - take the scaling
factor to be
the distance. That gives you a metric.

Think about it and you'll see that the usual metric,
the taxicab
metric, in fact all the L^p metrics, are special
cases of the metric
described here.

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for
email)

are you very hiddenly implying that you can rotate this metric afterall ?
or is it just my imagination ?

I don't know what it means to rotate a metric.

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)
.

Relevant Pages

  • Re: Thinking about metric spaces
    ... and declare that for all points on the ... the distance to the origin is 1. ... any two points move a copy of your convex set so its ... metric, in fact all the L^p metrics, are special ...
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  • Re: Thinking about metric spaces
    ... the distance to the origin is 1. ... any two points move a copy of your convex set so ... metric, in fact all the L^p metrics, are special ... I don't know what it means to rotate a metric. ...
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  • Re: Thinking about metric spaces
    ... and declare that for all points on the boundary of that set ... Then to find the distance between ... any two points move a copy of your convex set so its center is at ... metric, in fact all the L^p metrics, are special cases of the metric ...
    (sci.math)
  • Re: Thinking about metric spaces
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    (sci.math)
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