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Hello and welcome to Seoul for the answer to my
second chapter about
the hunter and the bear problem.
In my last problem I asked you if there were any other place on earth where you could go
South for 100 km, West for
another 100 km and
North for
another 100 km
and then get back,
back to your starting point.
North Pole does it
and my question was
if there were any other place.
The answer is...
The answer is:
Yes!
There are other places.
Let me introduce you to that line:
This is called
the Equator.
And the Equator is about
40,000 km long.
The interesting thing in this
is technically it's a
circle.
It's a circle so
the circumference of this circle is
40,000 km.
But as you can see, if I go further South
we can make other circles
a little bit like here
we can make other circles that are
actually of a smaller circumference
and all the way
to the South Pole
where the circumference is 0.
So we got
all the lengths we want from 40,000 km to 0
which means that somewhere here,
well, maybe there actually,
but somewhere here we can imagine there is a
circle
which circumference is
exactly
100 km.
So now
Let's think about it,
let's say that,
for the sake of my demonstration, this line,
I don't know if you can see it, here
which is
actually
which parallel is it?
The 40° parallel, let's say this line is
100 km long.
You can see it, it's here.
Of course it's not, in reality, but it doesn't matter
actually.
So let's say this line is the circle we're looking for
Now let's say that I start
100 km
above this line,
then I go
100 km South
then
I turn...
100 km West, which makes that I make a full turn
of that line
and I'm back
to where I started on that line and then I go back 100 km North
which is my starting point.
So actually there is not one place on Earth where I can do that:
all
those places,
the circle that is 100 km above the 100 km-circle,
all those places work, actually.
And if you think about it,
you can imagine that
instead of using in a 100-km circle
you can use
a 50
kilometer-
circle
because in that case if I start 100 km
higher,
I go down
and then
I will turn West
and that's going to make
two turns
then I go back up,
exactly two turns, and actually any circle
which circumference
is 100 divided by an integer
will work!
Well not the circle, 100 km above it.
So there's not one place that works,
there's that circle
and this circle
and thats circle, and this, and actually, there's
already for one circle there's an infinity of places.
And there's
technically
an infinity
of circles,
except that
of course
if you're in a circle
that's very very close to the South Pole, you might not want to turn
1,000 or 10,000 turns around. But still technically,
mathematically,
that works.
I hope you enjoyed that one
and see you next time for another
another problem
maybe geometry... I don't know
I have to think about it.
Bye! See you next time!