Question

I found the answer but I still don't understand the problem.

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: the North Pole is one point. there are infinitely many near the South Pole.

Answer 1

You get why the north pole right?

Answer 2

sorry i don't get it

Answer 3

ok
First the north pole...

Places near the north pole, you get South, east, and north making a Triangle like the attachment

Answer 4

get it?

Answer 5

oh ok thanks! so does this work the same way with the South Pole?

Answer 6

Now, if you think of the south pole, think of a circle (C1 in the attachment) wich has a circumference of 1 mile ok?
And lets say you start 1 mile north of this circle. You go south that 1 mile and you are at the border of the circle. If you go east 1 mile (and the cirle is 1 mile round) you will turn aroung and get to the same place you started. And you walk north again and you get to the same place you started your jurney. like in the attachment

Answer 7

Get it?

Answer 8

yes! yes! I get it! thank you so much

Answer 9

Now, the answer you get it says that there is an infinity of places in the south pole, it is true, think of the same answer as last, but instead of having a Circle of 1mile round, you will get a circle of 1/2 mile round. So, you start a mile north the cirlce. You go south one mile, east 1 mile; this time goin around the cirlce 2 times, and then north 1 mile.

And this applies infinetely, using a circle of 1/4 of a mile, 1/8 of a mile... basically any fraction. The only thing is that you would have to go around this more times.

Answer 10

Thank you so much for the help :)

Answer 11

you are welcome.. take care