Earth's surface puzzle

[The Wrath]

How many points are there on the Earth's surface, where you can do the following:

1.) Go one mile south.

2.) Go one mile east.

3.) Go one mile north, and end up at your starting point.

[dwwoelfel]

1?

[Lord Poppycock]

Yes, that’s the North Pole.

[punk]

The correct answer is there are an infinite number of such points.

One point is the north pole

Also any point a distance of 1 + 1/pi miles from the south pole works as well. From one of these points you go south a mile, then going east you make a circle with the south pole at the center, and then going north you return to your starting point.

Okay the above is to pretty good approximation assuming we can treat the region around the south pole as a plane, of course the earth is a sphere, but you get the idea

Edited February 23, 2005 by punk

[The Wrath]

I've never heard the explanation you just gave, but here's the one I've heard. Pick a place near the South Pole, where the circumference of the Earth is exactly one mile. Go one mile north of that and let that be your starting point. No you go south a mile, east a mile (which takes you all the way around the Earth) and north a mile, and you wind up at the same starting point. It also works for any latitude where the Earth's circumference is 1/2, 1/3, 1/4, etc. of a mile. So, the correct answer to this question is (infinity)*(infinity)+1.

[punk]

My explanation would be equivalent to the one say we should find a place where the circumference around south pole is one mile, and then go one mile north. So I was missing all the answers with circumferences of less than one mile.

However since infinity*infinity + 1 is infinity, I still got the right total number.

[JMeganSnow]

This Brain Teaser appeared in Marilyn Vos Savant's Parade column some time ago, and she put it and her answer in her book Of Course I'm for Monagamy! I'm also for everlasting peace and an end to taxes.

(Infinity is the right answer, btw.)

[The Wrath]

My explanation would be equivalent to the one say we should find a place where the circumference around south pole is one mile, and then go one mile north.  So I was missing all the answers with circumferences of less than one mile.

However since infinity*infinity + 1 is infinity, I still got the right total number. 

I wasn't sure if that's what you were saying or not...I think it threw me off when you put something about pi in there.