OK John. The north pole is the '1' solution.
now go to the south pole. take every circle above the south pole that
has a perimeter of a mile, or a whole fraction of a mile (like 1/2 or
1/3 or 1/4 ...). Any point one mile north of that will also satisfy your
definition.
I hope I made myself clear in english here.
Gil.
Gil,
I dont see your point. What do you mean by circle? Do you mean
the parallel? Imagine your home is one mile north from the south
pole. You travel south one mile. How do you travel east from there?
You cant go east or west.
Next, Imagine you are 1/2 mile north from the south pole. You
can't travel one mile south?
The furthest you can go is 1/2 mile south. Traveling in the same
direction would be traveling north.
John
John
John,
I am not good at explaining this. Suppose you are a little over 1 mile
north of the south pole.
you go down south one mile. still above the south pole. yo go east
and you are so close to the south pole that one mile is enough to
make a full circle (parallel could be the name yes) . Or even two or
three full circles (if you are close enough to the pole). so you would
arrive at the same point again, go up one mile north and be at your
starting point. Gil.
Ok, perhaps I can help explain. It's a bit long, so only read if you're
masochistic.
Latitudes, as I'm sure you all know, run parallel to the equator. The
equator, for your reference, has a circumference of 24,902 miles. This
means that if you are at the equator, and you walk due east, you will
be back where you started after you walk 24,902 miles. Thus, the line
of latitude that is the equator is 24902 miles long.
Lines of latitude get shortter as you approach the poles. (Think about
it.) There is one line of latitude that is a mile lpng. This means that if
you walk east, you'll be back where you started after you walk a mile.
This line of latitude is actually about 1/6th of a mile north of the south
pole (to be exact, it's 1/2Pi miles away) so you'll be walking in a
noticeable circle while technically traveling due east!
The point is, that at this line of latitude, walking 1 mile east takes you
back where you started. If your house is a mile north of this point,
then there you go! So, you start out at your house, walk 1 mile south,
then when you walk east, you make a circle around the south pole and
end up where you started. Walk 1 mile north and you get back to your
house.
Now, what about the 1/2, 1/3, etc?
Well, if you're at a line of latitude whose length is 1 mile, there is
another one (closer to the south pole) whose length is 1/2 mile. If you
wale east (You'll actually be walking in what is obviously a circle. In
fact, you'll be within yelling distance of the South Pole!) for 1/2 mile,
you'll be back where you started. Walk another 1/2 mile, you're back
where you started.
1/2 + 1/2 = 2/2 = 1
So, walk a mile east, you go round twice and end up at the same
place.
Same thing for all the other fractions.
Ok, did that help?
--Rein
