# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Geographical Center Problem
From: Steven Tripp
Date: 2001 Jul 25, 1:04 AM

```On 7/25/01 12:52 PM, "Dan Allen"  wrote:

> I have summarized the results so far on a new web page of mine.
>
>
> The center is currently located somewhere in Hudson Bay, which for some
> reason doesn't seem right.  I am going to keep studying this interesting
> geographical problem.

Given a set of locations you can generate a matrix consisting of distances
between location n1 and n1...nx, n2 and n1...nx, etc.

The sum of the rows will be the total distance between one location and all
the others.

Sample data based on "perceived distances" between American cities.

0    2.93    1.37    0.67    1.56    2.3    2.68    2.03    1.51    0.83
Atlanta    15.05
2.93    0    2.6    3.35    2.2    0.92    0.62    0.96    2.6    2.97
Seattle    16.18
1.37    2.6    0    1.5    1.09    2.97    2.6    2.34    0.46    0.55
NewYork    14.93
0.67    3.35    1.5    0    2.15    2.61    3.13    2.8    1.64    1.25
Miami    17.85
1.56    2.2    1.09    2.15    0    2.39    2.04    1.29    1.32    1.39
Chicago    14.04
2.3    0.92    2.97    2.61    2.39    0    0.37    0.92    3.26    2.68
LosAngeles    15.74
2.68    0.62    2.6    3.13    2.04    0.37    0    0.91    2.74    2.55
SanFrancisco    15.09
2.03    0.96    2.34    2.8    1.29    0.92    0.91    0    2.55    2.22
Denver    13.8
1.51    2.6    0.46    1.64    1.32    3.26    2.74    2.55    0    0.81
Boston    16.08
0.83    2.97    0.55    1.25    1.39    2.68    2.55    2.22    0.81    0
WashDC    15.25

Denver is the most central and Miami is the most non-central.

This assumes you use only known locations.

Steve Tripp
```
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