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(2): Doesn't matter. by Happy)
I thought of Achilles and the Turtle myself when i saw this, perhaps the distance is finite. Still the reasoning you use to determine its value seems uncertain. Im not sure you can apply euclidean principles (ie the trigonometry you use) to a curved geometry.
(eg the "north" you mention is not well defined in flat
terms, so you cannot use it in the construction of your
triangle)
"the traveller is following the hypoteneuse of a 1-1-2 right triangle with a height of 10,002 km"
again i doubt this. the traveller does not follow a right
triangle, since there is curvature involved.
re(3): Doesn't matter.
