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(7): Doesn't matter. by Cheradenine)
Near the pole, we can approximate the situation with polar coordinates. Consider a particle following a parametric curve in polar coordinates: r(t)=10-t, theta(t)=1/(10-t). At no point is the velocity of the particle pointed toward the pole. However, at t=10, we have r(t)=0, which is located smack-dab on the pole, regardless of the value of theta (which happens to be undefined at this point). In this case, despite wacky angular movement, the particle still winds up at the pole at a well-defined time.
re(8): Doesn't matter.
