Question

A woman starts at a point P on the earth's surface and walks 1 mi south, then 1 mi east, then 1 mi north, and finds herself back at P, the starting point. Describe all points P for which this is possible (there are infinitely many).

Answer 1

P has to be the North pole...
because of the earth's surface being a near sphere, and all longitudes meeting at the poles.....

Answer 2

Been there, done this, North South Pole etc---tulip235

Answer 3

The poles are not the right answer.

Answer 4

or, more accurately, the poles are not the only answer.

Answer 5

P must either be the north or south pole, or be any point such that 1 mile directly south of the starting point, the latitude of the Earth has a perimeter of exactly 1 mile.

Answer 6

is there a way to prove this mathematically?

Answer 7

*The line of latitude.

Answer 8

Identify the starting points.

Answer 9

Or one of them.

Answer 10

It should be self-evident. Obviously, the north and south travel negate one another with regards to final location, the only question is where on the Earth can one travel one mile east and end at the same point.
The poles are obvious solutions because if you start at them, you return to them regardless of how far east or west you travel. (Actually, technically the south pole might not be a valid answer since you can't travel south from it).
Then, you just need to figure out what other points satisfy the criteria - the only ones are those where traveling one mile east returns you to the same line of longitude you started at.

Answer 11

I know where the poles are, I am asking you to identify a place (one I can look at on a map):-)

Answer 12

Yes, but your question isn't the one I was answering.

Answer 13

From the North Pole you can descend south all round the central Pole Point , then walk as directed and you will land back at the pole...

Answer 14

South Pole is ruled out as you can't go south of the south pole....

Answer 15

All this including the i mile fro m South pole etc was already done here with diagrams:

http://openstudy.com/users/tulip235#/users/tulip235/updates/4e205f2b0b8b4841c1ab1c49

Answer 16

There you go, that's the right answer, and nicely formatted and everything.

Answer 17

ive already been looking at that..thanks..