A mathematical puzzle? [Resolved]

[mendhak]

I think this is a mathematical puzzle. I don't know the answer, but it involves maths, so I am posting here:



How many starting points are there on the Earth such that if a person traveled one mile south, one mile east and one mile north (s)he would end up in the placed that (s)he started at?


Help.

[Acidic]

not maths, logic.
there is one point, the north pole.

[twanvl]

Actually, there is a line near the south pole with a perimiter of exactly one mile, if you start anywhere 1 mile norht of that line you will also end up in the same place.

[Acidic]

oh yes. so then an infinite number of points. it took me a while to see what you meant.

[mendhak]

Sorry, kinda lost me there.

Can you explain, how are there an infinite number of points?

[wossname]

Originally posted by twanvl
Actually, there is a line near the south pole with a perimiter of exactly one mile, if you start anywhere 1 mile norht of that line you will also end up in the same place.

To clarify, a perfect circle with a circumference of exactly 1 mile centred at the south pole.

Starting at Point A which is exactly 1 mile north of the circle, we move south to the circle (Point B). Then we go east 1 mile which brings us full circle back to point B, then going north again takes us back to the start. Nice.

There are an infinite number of Point A's that are 1 mile north of the circle. Infinity is the answer

[wossname]

To illustrate...

[mendhak]

I get it now!

That means we could also start off at the North Pole, and end up on the North pole as well.

That gives us infinity+1 points

[Ecniv]

Sorry to post on resolved, but I don't get the 1 mile north of the south pole.

You don't end up at the same place.

The north pole makes sense.


Vince

[mendhak]

Originally posted by Ecniv
Sorry to post on resolved, but I don't get the 1 mile north of the south pole.

You don't end up at the same place.

The north pole makes sense.


Vince

The circumference of this circle around the south pole is 1 mile.

2*PI*R = 1 mile,

so R = 0.16 miles.

So, we start off at any point 1.16 miles from the south pole, walk south for 1 mile. You'll end up at the circle mentioned above. Now walk east for 1 mile. You'll end up at the same point you just joined the circle on.

Now walk one mile up north. You'll end up where you started.

[wossname]

Echo!
Echo!
Echo!
Echo!

[mendhak]

Hey, apparently your explanation (and efforts) weren't good enough for him.

Bow your head in shame.

[wossname]

I can't help it if people don't know the difference between radius and circumference. You 3 eyed gimp.

[Celest]

Just following on:

The circumference of the circle does not necessarily have to be 1 mile. It can also be half a mile, a third of a mile etc.

So there are (infinity*infinity) + 1 solutions

[alkatran]

I can see half a mile, but a third?

2*PI*R = 1 mile,so R = 0.16 miles.

Whoah... wait a second:

The radius of the earth is 6 380 kilometres

That means the circumference (of the largest possible circle) is 40 000 kilometres.

Wait.. maybe the radius was 3000 kilometres becaues that number should be 20 000....


Anyways my point was that you didn't include the earth in your calculations and 1.16 isn't necesarily right.

[Celest]

Originally posted by alkatran
I can see half a mile, but a third?

If the circumference is 1 mile then when you travel east you will travel one complete circle.

When it's half a mile you'll travel around twice and still return to the same position.

When it's a third of a mile you'll travel around three times but still return to the same position.

etc...

[alkatran]

Oh you meant as ending points for the circle, not start points. (1/2 is a valid start point)