Hi again everybody and welcome back from the summer!
My name is Jason, and one again this semester Collaborative Mathematics will
be releasing monthly video challenges.
If you are new to the project, you might want to check out our
"How It Works" video.
Otherwise, let's get right to it!
I was a mathematics teacher for a number of years in the United Stated, and
now I'm living in Oslo, Norway. And there's a lot that's different living abroad,
compared to living in the US.
But one of the things that's interesting is that in Norway, and in other countries too
around the world, we use a different size of paper than I was used to from the
United States.
So in the United States, you might be familiar with this size of paper. This is
called letter-sized paper in the US, but here in Norway and elsewhere, we use
this size paper. It's different. It's called a4 size paper, and if I line them up like this
you can see, maybe, that it's both wider and taller than a piece of
US letter-sized paper.
So that was interesting. The paper's different. Why not?
But the mathematics teacher in me got really excited about a4 paper because... I
like office products... but also because it has a very interesting property that when
you fold it in half width-wise, along its longest dimension, you get of course
another rectangle, a smaller rectangle.
But this smaller rectangle is
mathematically similar to the original one.
And that doesn't always happen. If you try that with a piece of letter-size paper
from the US. You fold it in half along its longer dimension, and of course you get
a smaller rectangle, but this smaller rectangle is not mathematically similar
to the original.
But it is for a4 paper, and that's something that makes a4 paper unique,
and it's something that I think is kind of cool.
OK, so here is the international paper challenge. Picture, if you will, a piece of
a4 paper that has the property I just described, and draw on it the largest
possible circle that you can.
The question is: what fraction of the paper is inside that circle?
In other words: What fraction of a piece a4 paper is enclosed by the largest circle
that can be drawn on that sheet?
So, that's the challenge and I'm looking forward to some response videos with
answers to that challenge.
And, there's another way to participate because I'm curious about the most
interesting piece of paper that you can find. We use different sizes of paper all
the time. Here at my desk I happen to have 3"-by-5" note cards. If you look
around your classroom, you might have different sizes of notecards, you might
have one of those big poster paper pads with really huge pieces of paper.
I'd like to hear what sorts of different, interesting paper you can find.
Look in your pocket. You might have some cash. Here's a US 5-dollar bill.
What fraction of a 5-dollar bill is enclosed by the largest circle that you
could draw on it?
Of course, I'm in Norway so we don't use dollars, we use kroner. This is a
100-kroner note, and you can see that it's almost the same height but it's quite a bit
shorter. What fraction of a Norwegian 100-kroner note is enclosed by the
largest circle you could draw on it?
You could ask that question about any piece of paper! So in your response
videos, answer my challenge, but then challenge us with the most interesting
piece of paper that you can find. Describe it and then ask that question about the
circle, about your piece of paper.
I look forward to seeing what you come up with and what happens next!
So go out there and have fun!