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 Solution by Cheradenine)

I agree that because a sphere can't be flattened like a cylinder can, the "straight" trig answer does not apply. I no longer see it as "counter-intuitive," though once it was pointed out that my first ipression bore a close similarity to the "paradoxes" of Zeno. I guess it's all a matter of perspective.

I do not, however, automatically accept the distance as simply C/4(√2) where C is the circumference of the sphere. (In this case C/4 would be the distance along a meridian from the Equator to the Pole.) I do accept that it is possible that it is a close approximation, if it can be shown that the sequence of circles of latitude I described in my last comment do converge.

Posted by TomM on 2002-10-01 11:51:39