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 Missing a bit of info... by friedlinguini)

It is obvious that he is approching the North Pole as the endpoint of his travel. What is not so obvious is that he will never quite arrive.

At any given point, his next step is in a direction 45° to the right of the direction to the pole. Eventually he winds up in an ever tightening spiral around the pole, but never reaces it.

The answers to the questions:

Where does he end up? Arbitrarily close to the North Pole. (Approaches that point as a limit)

How far did he go? An arbitrarily large number (Approaches aleph null as a limit)

How many times did he circumnavigate the earth? An Arbitrarily large number (Approaches aleph null as a limit)

Posted by TomM on 2002-09-25 15:18:17