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Subject: "South+West+North = Back"     Previous Topic | Next Topic
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Conferences The CTK Exchange High school Topic #349
Reading Topic #349
Claudio Buffara
Member since Aug-11-06
Aug-11-06, 00:12 AM (EST)
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"South+West+North = Back"
 
   The problem that starts this article:
<https://www.cut-the-knot.org/triangle/pythpar/NonEuclid.shtml>
is said to have a continuum of solutions but I was only able to find a denumerable set of them: the "obvious" one, starting at the North Pole and the ones near the South Pole where you go West on a parallel of length 10/n miles (you go around n times).
Are there any other solutions?

Best regards,
Claudio Buffara.


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alexbadmin
Charter Member
1871 posts
Aug-12-06, 00:21 AM (EST)
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1. "RE: South+West+North = Back"
In response to message #0
 
   What you found is a denumerable set of parallels. Since you can start from any point on any of the parallels, there is a continuum of starting points.

Just to make sure, the parallels whose union provides a continuum of solutions are located 10 miles North from the parallels of length 10/n.

Alex


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