Subject: Re: re anchorage & great circles & voronoi<br/>
Date: Oct 15, 2001 @ 14:02<br/>
Author: granthutchison@cs.com (granthutchison@...)<br/>
<a href="4090.htm">Prev</a>&nbsp;&nbsp;&nbsp;&nbsp;Post in Topic&nbsp;&nbsp;&nbsp;&nbsp;<a href="4096.htm">Next</a>&emsp;[<a href="topic4080.htm">All</a> Posts]<br/>
<a href="4092.htm">Prev</a>&nbsp;&nbsp;&nbsp;&nbsp;Post in Time&nbsp;&nbsp;&nbsp;&nbsp;<a href="4094.htm">Next</a><br/>
<br/><br/>
<div id="ygrps-yiv-1741035797">Michael:<br/>
<blockquote><span title="ireply"> &gt; & may i then safely conclude that the most capitally <br/>
&gt; distant populated place <br/>
&gt; on earth is the south pole<br/>
&gt; or might those crazy voronoi lines punish this <br/>
&gt; presumption somehow<br/>
 </span></blockquote>Well, my suggestion was very much just a first good counterexample to Anchorage. I&#39;m sure there&#39;s room for improvement in the northern hemisphere - although northern capitals reach higher latitudes than southern capitals, they do cluster in the Greenwich hemisphere. Seems to me the off-centre locations of Moscow, Ottawa and Washington would leave scope for us to head NW from Anchorage quite a ways before we began to approach a national capital. It might also be worth poking around the NE Pacific.<br/>
My maths isn&#39;t good enough to think of a way to type in lat and long of all 192 national capitals and get some equations to spit out the answer - in fact I wonder if this might be one of those travelling-salesman-type problems whose solution-time grows exponentially with the number of points considered. As Anton says, the point is going to be at a Voronoi vertex, and I think we could add that the edges meeting at that vertex must have a higher average length than at any other vertex on the globe, but I&#39;m not able to push any further forward than that.<br/>
Perhaps I can do a bit of my experimental geography, and just plot some nice big circles around some selected capitals, and see where I get. Graphics will (of course!) follow if I come up with anything informative.<br/>
<br/>
<blockquote><span title="ireply"> &gt; also<br/>
&gt; do we now have the ability to learn the farthest <br/>
&gt; point on earth from the sea<br/>
&gt; & the farthest from land<br/>
 </span></blockquote>If we could solve the above, we could certainly just plug in some Asian inlets or Pacific peninsulas and churn out an answer to these questions, too.<br/>
The land point is in Asia, obviously, and I know the old Tuvan S.S.R. contains an obelisk supposedly marking the centre of Asia. But if we take Europe into account, I imagine that would shift the balance-point westwards. (I&#39;ve also heard tell that the Tuvan obelisk is not correctly positioned in any case.)<br/>
<br/>
Grant</div>