math geo problem

How many places are there on Earth, so that if you go 1km north, 1km west and 1km south, you'll end up at exactly the same place

hint: there are more than one ... 😀

An infinite amount, assuming a set distance can be broken down into infinite smaller distances.

EDIT:spelling

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)

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)

Aha! This is an oldie but a goodie, just remembered the answer.

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. 😉

One classic puzzle of the same category is something like this:
"I am a hunter. I went 1 mile south, didn't find anything. Went 1 mile west, shot a bear. Went home again, having to carry the bear over my shoulder one whole mile."
Question, what colour had the bear?

The equator?

definitely not

Originally posted by PBE6
Aha! This is an oldie but a goodie, just remembered the answer.

Yes, quite neat, isn't it?

here 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)

1 = southhpole

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

Travel by air from the equator for 23 hours 59 minutes 58 seconds.

1.159 km from the North Pole?

Walk north towards the North Pole for 1 km, turn west and walk for 1 km (360 degrees), turn south and walk back 1 km to your point of departure.

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

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, ...

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, ...

Why would I have to divide the perimeter by pi to find the perimeter?

If 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.