- 07 Apr '08 14:06

Aha! This is an oldie but a goodie, just remembered the answer.*Originally posted by 3v1l5w1n***nope, you can't break it ... you have to walk 1km north THEN 1km west and THEN 1km sourth. Also, if you think there are infinitely many such places, can you described them (e.g. how to find them)**

The first point people think of is the South Pole. The second set of points is a bit trickier, but I'm sure most people can "wrap" their heads "around" it. - 07 Apr '08 15:40here is a hint:

there are basically two possibilities:

1.) You end up going in a equilateral triangle with all right angles (yes, it is possible and quite common on a sufrace of a sphere that inner angles of a triangle sum up to more than 180 degrees) - this is if you start from the South Pole.

2.) In this option you definitely won't be going in a triangle ... so what else can you do to come back to the same place (while changing the direction twice) - 07 Apr '08 17:01

quite close, actually i think you just forgot to devide by pi ... so*Originally posted by Mephisto2***1 = southhpole**

every point on every parallel near the north pole with a perimeter of 1/1, 1/2, 1/3, ... km

all the solutions can be described as this:

1.) the South Pole

2.) the union of concentric circles with the center at the North Pole and the radius r = ( 1 / 2 * pi * n ) + 1 where n is 1, 2, 3, ... - 07 Apr '08 17:33

Why would I have to divide the perimeter by pi to find the perimeter?*Originally posted by 3v1l5w1n***quite close, actually i think you just forgot to devide by pi ... so**

all the solutions can be described as this:

1.) the South Pole

2.) the union of concentric circles with the center at the North Pole and the radius r = ( 1 / 2 * pi * n ) + 1 where n is 1, 2, 3, ... - 07 Apr '08 21:29If the circumference at the longitude 1 km to the north from your starting point is of the form 1/k km, where k is an integer, then taking the path of 1 km North, 1 km West, and 1 km South will bring you back to your starting point. (You'll be in the same place bofore and after the second km travelled.)

I'm sure someone has given the formula for finding these longitudes.