Reason Behind the name for Jungle-River Metric.

analysismetric-spacesreal-analysisterminology

The Metric defined by $d(x,y)=|x_2-y_2|$ if $x_1=y_1$
and =$|x_2|+|y_2|+|x_1-y_1|$ if $x_1 \neq y_1$ ; where $x=(x_1,x_2)$ and $y=(y_1,y_2)$ is called the Jungle-River Metric.

Is there any special reason for calling this Metric by this name?

Best Answer

As it it explained here: imagine the $x$-axis as a river. Everywhere else, there are lots of plants, so that walking on any direction is very hard. So, your best option for going from $(a,b)$ to $(c,d)$ is:

  • to move “down” or “up” to meet the river at the point $(a,0)$
  • to sail along to the point $(c,0)$
  • then to go (again, “down” or “up”) through the jungle until you reach $(c,d)$.

This leads to the “distance” $|b|+|a-c|+|d|$.

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