A traveller starts out from the Earth's equator, heading exactly northeast. Undeterred by mountains, oceans and political boundaries, he continues on a northeasterly heading until he can go no further.
Where does he end up?
How far did he go?
How many times did he circumnavigate the earth? (For these purposes, this means travel through 360 degrees of longitude.)
(In reply to
re(4): Doesn't matter. by friedlinguini)
Yes, this may be true, but it is precisely the application
of this reasoning to a non infintesimal distance which i have
problems with. After all, it is extension of this reasoning
to the "macroscopic" realm that you useto reach an
answer. I find this extension itself the problem (due
to curvature)
On another more abstract line, i think i agree
with TomM:
Consider the travellerīs speed to be constant.
Add to this the fact that he will never get to
the north pole. Inevitably, there is no limit
to the distance that the traveler covers..
re(5): Doesn't matter.
