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(3): Doesn't matter. by Cheradenine)
I think it might help to think in terms of differential movement, rather than a finite right triangle. If the traveller moves northeast dS units, then he moves north and east each dS/√2 units. At a differential scale, the curvature of the earth makes no difference.
re(4): Doesn't matter.
