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
Doesn't matter. by TomM)
I disagree. I think you have a bit of a Xeno's Paradox thing going on here. The way I figure it, for every mile the traveller moves, he moves 1/√2 miles north and 1/√2 miles east. Assuming that the circumference of the earth is 24,000 miles, he must travel 6,000 miles north. Therefore, his total travel distance is 6,000√2 miles. It might be true that he runs through an infinite number of infinitely small orbits around the pole in the process (I haven't done the math here), but I think the total distance travelled is finite.
re: Doesn't matter.
